9.13: Current Issues in Corrections - War on Drugs and Gangs
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- Alison S. Burke, David Carter, Brian Fedorek, Tiffany Morey, Lore Rutz-Burri, & Shanell Sanchez
- Southern Oregon University via OpenOregon
The war on drugs, initiated by President Nixon in 1971, was framed as an all-out war to eradicate drugs in the United States. The massive expenditures on the curtailment of the drug epidemic also shifted our views on drug use. We became much more punitive towards drugs, treating it as more of a criminal justice issue, rather than as a substance dependence issue. Good or bad, drug use was demonized in the public and media, which aided in the development of much tougher sanctions on drug use in America. The Drug Enforcement Agency was created in 1973, to provide another arm of the government to tackle a specific issue, drugs. By the 1980s, lengthy sentences for drug possession were also in place. One to five-year sentences for possession were increased to upwards of 25 years. There was also an increased focus on gangs, which were held responsible for the majority of the drug trade in the United States.
Gang activity in the United States was prevalent long before the enactment of the war on drugs. However, once the linkages between our fear of crime, and the drug trade by gangs became more pronounced due to the war on drugs, the conflict escalated. While there are hundreds of different gangs in many neighborhoods and communities in the United States today, gangs in prison have converged into four main gangs, or what corrections call security threat groups. These four basic gangs include the Whites, the Blacks, the Southerners (Surenos, or EME), and the Northerners (Nortenos). Not only are these STGs considered violent inside and outside of prison, but they are also actively involved in the continuing drug trade in the United States today, even behind bars. In fact, many of the leaders of all of the gangs on the streets are held in one prison in California, Pelican Bay State Prison.
Within the prisons in the United States, gangs actively recruit members, communicate with gangs on the streets, run the drug trade, and are also at war with each other over the power within the institutions, from their perspective. There have been numerous documentaries on gangs in the U.S., and even mainstream films about gangs and gang life, both inside and out. A few notable examples of films to watch on this subject include Felon (2008), Shot Caller (2017), and American Me (1992).
Transcarceration
At the same time, the proliferation of gangs was occurring in prisons in the United States, there were another sizeable increase of prisoner type, mentally ill inmates. This is due to the transinstitutionalization that occurred for thousands during the late 1970s, 1980s. Transinstitutionalization, or transcarceration is a process that occurred for many with mental health issues when State-run mental health facilities began to close their doors. Having few choices of where to go, many became homeless or destitute. Ultimately, these individuals wound up in America’s jails and prisons. This is also compounded by how we have shifted our views on the mentally ill within the courts and justice system. While insanity is a defense that is used in court, it is rare (roughly 1% of cases), and even more rarely does it conclude in success. This shift occurred within our understanding of guilt surrounding mental illness. In the past, an individual would be held not guilty by reason of insanity. However, this shifted to guilty, but legally insane. The guilt would be grounds to still incarcerated individuals. Changes in policy like this also contributed to the increase in offenders in the 1980s.
Get Tough Policies
Another reason for the large scale increases can be found in our changes to policies surrounding sentences and sentence lengths. Get tough policies flourished in the latter half of the 1980s and into the 1990s. This included truth in sentencing legislation three-strikes policies, and drug crime minimums. Truth in sentencing, also known as the 85% rule, is where mandatory minimums of sentences would be forced to be served by incarcerated individuals. Thus if an individual was sentenced to prison, a mandatory minimum of 85% of the sentence would have to be served before the individual was eligible for release (parole). This added to the average length of sentences served in American prisons, which meant that individuals were not being released as early as in prior years. Thus, as more individuals were coming in due to increases in other legislation, there were already more people in the prisons.
Three strikes policies were enacted in many States. In 1993, Washington overwhelmingly passed (75% voted yes) to approve initiative 593 [1] This policy increased sentence lengths for 40 felonies, which included life imprisonment. Perhaps the largest 3 strikes policy was in 1994, in California, with Proposition 184, commonly called the Three Strikes and You’re Out policy. It mandated a minimum of 25 years of prison for individuals committing 3 felonies. What made this policy more pervasive than others was the way in which it could be applied. If a person had two previous strikes for violent, or serious felonies (not necessarily violent), any new felony was life imprisonment, with a minimum of 25 years. For a more detailed view of this policy, see https://lao.ca.gov/2005/3_strikes/3_strikes_102005.htm
Drug laws were also changing at this time. The Controlled Substances Import and Export Act (1970), started the increases for drugs in the U.S. under federally mandated minimums found within the federal code 21 U.S.C. § 841. For a detailed reporting of these minimums, see https://www.ussc.gov/sites/default/files/pdf/research-and-publications/research-publications/2017/20171025_Drug-Mand-Min.pdf
One of the most debated issues within the drug sentencing laws was the differential between cocaine (in powder form) and crack ( also form of cocaine, diluted and in a hardened paste form). During the increases in sentencing, there was a disparity in the lengths of sentences for comparable weights of these two drugs. There has been much debate whether this targeted poorer individuals more harshly, as crack was seen as a poor man’s cocaine. However, with additional mandatory minimum increases in the 1980s, differences in sentence lengths began to widen. In a detailed report, Barbara Meierhoefer (1992) detailed how the average sentence lengths for African Americans (for similar weights of crack v. cocaine for Whites) was roughly 50% higher, supporting this assertion that drug sentences were not equal. [2]
With over a million arrests per year for drugs, it does add to the prison system as a whole. While the proportion of drug offenders in State prisons hovers around 20-25%, it is much larger at the federal level. As seen below, it makes up over half of the federal prisons. In all, the drug seriousness went up (how drugs are scheduled within federal guidelines), and sentence lengths for drugs went up; certain drugs more than others also went up.
- Wright, P. (1995). Three strikes racks ‘em up. Journal of Prisoners on Prisons, 6 (2), 3-6. https://www.ncjrs.gov/App/Publications/abstract.aspx?ID=162918 ↵
- Meierhoefer, B. (1992). The general effect of mandatory minimum prison terms: A longitudinal study of federal sentences imposed. Federal Judicial Center . www.fjc.gov/sites/default/files/2012/GenEffMM.pdf ↵


9.6: Bonding in TiS₂, MoS₂, and Pyrite Structures
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Many layered dichalcogenides, such as TiS 2 and ZrS 2 , have the CdI 2 structure. In these compounds, as we have noted above, the metal ions are octahedrally coordinated by S. Interestingly, the structures of MoS 2 and WS 2 , while they are also layered, are different. In these cases, the metal is surrounded by a trigonal prism of sulfur atoms. NbS 2 , TaS 2 , MoSe 2 , MoTe 2 , and WSe 2 also have the trigonal prismatic molybdenite structure, which is shown below alongside a platy crystal of MoS 2 .
The coordination of the metal ions by a trigonal prism of chalcogenide ions is sterically unfavorable relative to octahedral coordination. There are close contacts between the chalcogenide ions, which are eclipsed in the stacking sequence AbA/BaB/AbA/BaB ... (where "/" indicates the van der Waals gap between layers). What stabilizes this structure?
The molybdenite structure occurs most commonly in MX 2 compounds with a d 1 or d 2 electron count . The figure below compares the splitting of d-orbital energies in the octahedral and trigonal prismatic coordination environments:
The trigonal prismatic structure is stabilized in MoS 2 by filling the lowest energy band, the d z2 . The d z2 orbital which points vertically through the triangular top and bottom faces of the trigonal prism, has the least interaction with the sulfide ligands and therefore the lowest energy. The d xz and d yz orbitals, which point at the ligands, have the highest energy. The d z2 orbital is lower in energy in this structure than the t 2g orbitals are in the octahedral structure of TiS 2 .
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d-orbital splittings and energy bands in TiS 2 and MoS 2 . MoS 2 is a semiconductor with a 1.3 eV gap between its filled and empty bands. |
Because it has an unfilled t 2g band, TiS 2 is relatively easy to reduce by intercalation with Li. For this reason, LiTiS 2 was one of the first intercalation compounds studied by Stanley Whittingham, who developed the concept of the non-aqueous lithium ion battery in the early 1970's. [3] Because it has a filled d z2 band, MoS 2 is harder to reduce, but it can be intercalated by reaction with the powerful reducing agent n-butyllithium to make Li x MoS 2 (x < 1). Atoms in the van der Waals planes of these compounds are relatively unreactive, which gives MoS 2 its good oxidative stability and enables its application as a high temperature lubricant. Atoms at the edges of the crystals are however more reactive and in fact are catalytic. High surface area MoS 2 , which has a high density of exposed edge planes, is used as a hydrodesulfurization catalyst and is also of increasing interest as an electrocatalyst for the reduction of water to hydrogen.
Layered metal dichalcogenides, including MoS 2 , WS 2 , and SnS 2 , can form closed nanostructures that take the shape of multiwalled onions and multiwalled tubes. These materials were discovered by the group of Reshef Tenne in 1992, shortly after the discovery of carbon nanotubes. Since then nanotubes have been synthesized from many other materials, including vanadium and manganese oxides.
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The pyrite (FeS 2 ) crystal structure. The structure is related to NaCl, with Fe 2 + and S 2 2 - ions occupying the cation and anion sites. |
Although early (TiS 2 ) and late (PtS 2 ) transition metal disulfides have layered structures, a number of MS 2 compounds in the middle of the transition series, such as MnS 2 , FeS 2 and RuS 2 , have three-dimensionally bonded structures. For example, FeS 2 has the pyrite structure , which is related to the NaCl structure. The reason is that FeS 2 is not Fe 4 + (S 2- ) 2 , but is actually Fe 2 + (S 2 2 - ), where S 2 2 - is the disulfide anion (which contains a single bond like the peroxide anion O 2 2 - ). S 2- is too strong a reducing agent to exist in the same compound with Fe 4 + , which is a strong oxidizing agent. Because FeS 2 is actually Fe 2 + (S 2 2 - ), it is a 1:1 compound and adopts a 1:1 structure.


4.6: Chapter 4 Summary
After selecting and refining the speech topic, the next most important consideration is to determine how that topic will be received by the intended audience. This reflects the principle of audience-centered speaking, or the act of carefully and mindfully tailoring one’s presented information to the knowledge levels, beliefs, values, and opinions of the audience. As a means to adapt the information to an audience in this manner, speakers must first start with collecting information from that audience. This data collection can happen passively (eavesdropping, public information, conversations prior to the speech, etc.) or actively (interviews, surveys, etc.), but ultimately, presenters must find out what the audience knows or does not know about the topic, and also, how they feel about the topic (attitudes, opinions, beliefs, values, etc.). Once they know what the audience knows and how they feel about the topic, then speakers can work further to refine what information makes it into their presentation, as well as how it gets presented so that the audience memorably understands the message as originally intended.


12.9: Bibliography
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- Jennifer Hasty, David G. Lewis, & Marjorie M. Snipes
- OpenStax
Amadiume, Ifi. 1987. Male Daughters, Female Husbands: Gender and Sex in an African Society . London: Zed Books.
Barnes, Melissa L., Alexis Adams-Clark, Marina N. Rosenthal, and Carly P. Smith. 2021. “Pledged into Harm: Sorority and Fraternity Members Face Increased Risk of Sexual Assault and Sexual Violence.” Dignity: A Journal of Analysis of Exploitation and Violence 6 (1). https://doi.org/10.23860/dignity.2<IP_ADDRESS> .
Behrens, Kevin G. 2020. “A Principled Ethical Approach to Intersex Paediatric Surgeries.” BMC Medical Ethics 21:108. https://doi.org/10.1186/s12910-020-00550-x .
Bonvillain, Nancy. 1995. Women and Men: Cultural Constructs of Gender . Englewood Cliffs, NJ: Prentice Hall.
Brandes, Stanley. 1980. Metaphors of Masculinity: Sex and Status in Andalusian Folklore . Philadelphia: University of Pennsylvania Press.
Butler, Judith. 1992. “The Body You Want: An Interview with Judith Butler.” By Liz Kotz. Artforum , November 1992. https://www.artforum.com/print/19920...h-butler-33505 .
Dankwa, Serena Owusua. 2009. “‘It’s a Silent Trade’: Female Same-Sex Intimacies in Post-Colonial Ghana.” NORA: Nordic Journal of Feminist and Gender Research 17 (3): 192–205. https://doi.org/10.1080/08038740903117208 .
Evans-Pritchard, E. E. 1970. “Sexual Inversion among the Azande.” American Anthropologist 72 (6): 1428–1434. https://doi.org/10.1525/aa.19<IP_ADDRESS>a00170 .
Fausto-Sterling, Anne. 1992. Myths of Gender: Biological Theories about Women and Men . 2nd ed. New York: Basic Books.
Fausto-Sterling, Anne. 2000. Sexing the Body: Gender Politics and the Construction of Sexuality . New York: Basic Books.
Fausto-Sterling, Anne. 2001. “A Conversation with Anne Fausto-Sterling: Exploring What Makes Us Male or Female.” Interview by Claudia Dreifus. New York Times , January 2, 2001. https://www.nytimes.com/2001/01/02/s...or-female.html .
Fedigan, Linda Marie, and Laurence Fedigan. 1989. “Gender and the Study of Primates.” In Gender and Anthropology: Critical Reviews for Research and Teaching , edited by Sandra Morgen, 41–64. Arlington, VA: American Anthropological Association.
Gibbons, Ann. 2012. “Bonobos Join Chimps as Closest Human Relatives.” Science , June 13, 2012. https://www.sciencemag.org/news/2012...uman-relatives .
Gibbons, Ann. 2020. “Woman the Hunter: Ancient Andean Remains Challenge Old Ideas of Who Speared Big Game.” Science , November 4, 2020. https://www.sciencemag.org/news/2020...eared-big-game .
Gimbutas, Marija. 1991. The Civilization of the Goddess: The World of Old Europe . Edited by Joan Marler. San Francisco: HarperSanFrancisco.
Gutmann, Matthew C. 1997. “Trafficking in Men: The Anthropology of Masculinity.” Annual Review of Anthropology 26:385–409.
Gyasi-Gyamerah, Angela Anarfi, and Mathias Søgaard. 2020. “Caught between Worlds: Ghanaian Youth’s Views of Hybrid Sexuality.” In Routledge Handbook of Queer African Studies , edited by S. N. Nyeck, 254–265. New York: Routledge.
Heller, Alison. 2019. Fistula Politics: Birthing Injuries and the Quest for Continence in Niger . New Brunswick, NJ: Rutgers University Press.
Herdt, Gilbert H., ed. 1984. Ritualized Homosexuality in Melanesia . Berkeley: University of California Press.
Hewlett, Barry S. 1991. Intimate Fathers: The Nature and Context of Aka Pygmy Paternal Infant Care . Ann Arbor: University of Michigan Press.
Howe, Cymene. 2015. “Queer Anthropology.” In International Encyclopedia of the Social and Behavioral Sciences , edited by James D. Wright, 2nd ed., 752–758. New York: Elsevier. https://doi.org/10.1016/B978-0-08-097086-8.12219-6 .
Lancaster, Roger N. 1992. Life Is Hard: Machismo, Danger, and the Intimacy of Power in Nicaragua . Berkeley: University of California Press.
Lipset, David. 2003. “Rereading Sex and Temperament: Margaret Mead’s Sepik Triptych and Its Ethnographic Critics.” Anthropological Quarterly 76 (4): 693–713.
Malinowski, Bronislaw. 1929. The Sexual Life of Savages in North-Western Melanesia: An Ethnographic Account of Courtship, Marriage, and Family Life among the Natives of the Trobriand Islands, British New Guinea . London: George Routledge & Sons.
Mascia-Lees, Frances E., and Nancy Johnson Black. 2000. Gender and Anthropology . Prospect Heights, IL: Waveland Press.
Mead, Margaret. 1928. Coming of Age in Samoa: A Psychological Study of Primitive Youth for Western Civilisation . New York: W. Morrow.
Mead, Margaret. 1935. Sex and Temperament in Three Primitive Societies. New York: W. Morrow.
Nanda, Serena. 2000. Gender Diversity: Crosscultural Variations . Prospect Heights, IL: Waveland Press.
Newton, Esther. 1972. Mother Camp: Female Impersonators in America . Englewood Cliffs, NJ: Prentice-Hall.
Newton, Esther. 2000. Margaret Mead Made Me Gay: Personal Essays, Public Ideas . Durham, NC: Duke University Press.
Newton, Esther. 2018. My Butch Career: A Memoir . Durham, NC: Duke University Press.
Newton, Esther. 2019. “Esther Newton Talks My Butch Career: A Memoir .” October 3, 2019, in Outtake Voices , hosted by Charlotte Robinson. Podcast. https://voices.outtakeonline.com/201...ch-career.html .
Ochoa, Marcia. 2014. Queen for a Day: Transformistas, Beauty Queens, and the Performance of Femininity in Venezuela . Durham, NC: Duke University Press.
Ozyegin, Gul, ed. 2015. Gender and Sexuality in Muslim Cultures . Burlington, VT: Ashgate.
Rosaldo, Michelle Zimbalist. 1974. “Woman, Culture, and Society: A Theoretical Overview.” In Woman, Culture, and Society , edited by Michelle Zimbalist Rosaldo and Louise Lamphere, 17–42. Stanford, CA: Stanford University Press.
Sanday, Peggy Reeves. 1990. Fraternity Gang Rape: Sex, Brotherhood, and Privilege on Campus . New York: New York University Press.
Smith, Daniel Jordan. 2017. To Be a Man Is Not a One-Day Job: Masculinity, Money, and Intimacy in Nigeria . Chicago: University of Chicago Press.
Tringham, Ruth. 1993. Review of The Civilization of the Goddess: The World of Old Europe , by Marija Gimbutas, edited by Joan Marler. American Anthropologist 95 (1): 196–197.
Viloria, Hida. 2017. “Doctors Resort to Nonsensical Reasoning to Justify Surgeries on Intersex Children.” HuffPost , July 29, 2017. https://www.huffpost.com/entry/docto...b09982b7376474 .
Weston, Kath. 1991. Families We Choose: Lesbians, Gays, Kinship . New York: Columbia University Press.
Zihlman, Adrienne L. 1997. “Natural History of Apes: Life-History Features in Females and Males.” In The Evolving Female: A Life History Perspective , edited by Mary Ellen Morbeck, Alison Galloway, and Adrienne L. Zihlman, 86–104. Princeton, NJ: Princeton University Press.


46.2: If Our Class Were the World
Lesson
Let's use math to better understand our world.
Exercise \(\PageIndex{1}\): All 7.4 Billion of Us
There are 7.4 billion people in the world. If the whole world were represented by a 30-person class:
- 14 people would eat rice as their main food.
- 12 people would be under the age of 20.
- 5 people would be from Africa.
- How many people in the class would not eat rice as their main food?
- What percentage of the people in the class would be under the age of 20?
- Based on the number of people in the class representing people from Africa, how many people live in Africa?
Exercise \(\PageIndex{2}\): About the People in the World
With the members of your group, write a list of questions about the people in the world. Your questions should begin with “How many people in the world. . .” Then, choose several questions on the list that you find most interesting.
Exercise \(\PageIndex{3}\): If Our Class Were the World
Suppose your class represents all the people in the world.
Choose several characteristics about the world’s population that you have investigated. Find the number of students in your class that would have the same characteristics.
Create a visual display that includes a diagram that represents this information. Give your display the title “If Our Class Were the World.”


4.2.5I: The Division of Labor
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Division of labor is the specialization of cooperative labor in specific, circumscribed tasks and similar roles.
Learning Objectives
- Interpret Durkheim’s division of labor theory in terms of mechanical and organic solidarity, as well as progression from primitive to advanced societies
Key Points
- An increasingly complex division of labor is historically closely associated with the growth of total output and trade, the rise of capitalism, and of the complexity of industrialization processes.
- Durkheim classified societies as primitive or advanced based on their division of labor.
- According to Durkheim, in primitive societies where there is little or no division of labor, people act and think alike with a collective conscience. In advanced societies with high division of labor, social ties are relatively homogeneous and weak.
- Labor hierarchy is a very common feature of the modern workplace structure.
- It is often agreed that the most equitable principle in allocating people within hierarchies is that of true competency or ability. This important Western concept of meritocracy could be interpreted as an explanation or as a justification of why a division of labor is the way it is.
Key Terms
- industrialization : A process of social and economic change whereby a human society is transformed from a pre-industrial to an industrial state
- meritocracy : Rule by merit, and talent. By extension, now often used to describe a type of society where wealth, income, and social status are assigned through competition.
- labor hierarchy : Labor hierarchy is a very common feature of the modern workplace structure, but of course the way these hierarchies are structured can be influenced by a variety of different factors.
Division of labor is the specialization of cooperative labor in specific, circumscribed tasks and roles. Historically, an increasingly complex division of labor is closely associated with the growth of total output and trade, the rise of capitalism, and of the complexity of industrialization processes. Division of labor was also a method used by the Sumerians to categorize different jobs and divide them between skilled members of a society.
Emilie Durkheim was a driving force in developing the theory of the division of labor in socialization. In his dissertation, Durkheim described how societies maintained social order based on two very different forms of solidarity (mechanical and organic), and analyzed the transition from more “primitive” societies to advanced industrial societies.
 In such a society, Durkheim viewed crime as an act that “offends strong and defined states of the collective conscience”. Because social ties were relatively homogeneous and weak throughout society, the law had to be repressive and penal, to respond to offenses of the common conscience.
In an advanced, industrial, capitalist society, the complex division of labor means that people are allocated in society according to merit and rewarded accordingly; social inequality reflects natural inequality. Durkheim argued that in this type of society moral regulation was needed to maintain order (or organic solidarity). He thought that transition of a society from “primitive” to advanced may bring about major disorder, crisis, and anomie. However, once society has reached the “advanced” stage, it becomes much stronger and is done developing.
In the modern world, those specialists most preoccupied with theorizing about the division of labor are those involved in management and organization. In view of the global extremes of the division of labor, the question is often raised about what manner of division of labor would be ideal, most efficient, and most just. It is widely accepted that the division of labor is to a great extent inevitable, simply because no one can perform all tasks at once. Labor hierarchy is a very common feature of the modern workplace structure, but the structure of these hierarchies can be influenced by a variety of factors.


7.1: Clarifying Your Vision, Mission, and Goals
By the end of this section, you will be able to:
- Clarify the vision statement, mission statement, and goals for your enterprise
- Define and develop a problem-solution narrative that is compelling
- Define and develop a value proposition that is credible and appealing to customers and investors
Entrepreneurs can sometimes be compared to superheroes: They solve problems. They wield great power and responsibility. They’re willing to take on risks the way superheroes are willing to take on villains. They are undaunted in the face of failure. They seek solutions and continuous improvement of their products with their customers in mind so that their solutions go beyond addressing their individual needs. When an entrepreneur succeeds, others say “If only I’d thought of that!”
But thinking isn’t enough. And even doing isn’t enough. Successful entrepreneurs also understand the need to communicate the origin and value of their venture. They not only solve problems, they tell stories of crises averted, foes bested, and painful defeats from which they learned how to start anew. After all, what’s a hero without an origin story and a list of tales, battles lost, and markets won?
In superhero narratives, these origin stories are sacred lore. For an entrepreneur, a problem-solution narrative is like the origin story for their offering. The problem-solution narrative concisely introduces a specific problem that affects many people and presents the good or service as an innovative, unique, and insightful solution. Here are some classic problem-solution narratives in advertising and in corporate origin stories to think about as you consider how to craft a quick, compelling problem-solution narrative.
- A young man starting high school lacks muscle mass. He drinks milk and gets stronger, earning the respect of his classmates.
- Young people, pictured in silhouette, walk around a city looking bored with life. Then, they turn on their new MP3 players and start dancing in the streets. Their world is set ablaze in color and sound.
- A man literally turns into Joe Pesci when he gets hungry.
These may not be the greatest stories ever told. You’re not going to get a National Book Award for a Snickers commercial, but these are memorable narratives about people who have a problem that the product in question can solve.
To stay focused through repeated series of successes and failures, you need more than a problem-solution narrative: You need a vision and, in turn, a mission statement and goals. You learned about these in The Entrepreneurial Perspective , but you should revisit them as you develop your story and refine how to pitch that story to potential investors, customers, and employees.  It is delivered (usually) to potential investors in a startup. More on pitches later in the chapter.
Sara Minkara’s vision statement may be defined as wishing to live in a world where visually impaired people are not discriminated against. Her venture’s mission is to establish a well-functioning nonprofit organization showing people in the United States, the Middle East, and North Africa the humanity and value in those with severely impaired eyesight. Minkara’s vision , imagining the organization’s long-term future, is to make it a global leader in providing services to visually impaired people. Specific goals include hosting events, developing educational programs, organizing awareness campaigns, and, of course, fundraising. Following this example of mission, vision, and goals, let’s break down each concept and consider how they work broadly and apply to your potential venture.
Vision
A vision statement, as you saw in The Entrepreneurial Perspective , outlines the venture’s broader purpose, what the entrepreneur sees the venture growing into in the future. Before you can create a focused mission statement and goals answering who you are, what you do, and what you plan to do in the future, you must develop a vision statement that allows you look into the future to answer this question: “What might we become someday if our organization were the best possible version of itself?”
Drafting a vision statement is an exercise in ideation —a purposeful process of opening up one’s mind to new trains of thought that branch out in many directions from a stated purpose or problem—in this case, with the goal of generating new possibilities for goods, services, or processes to make your venture sucessful. A vision statement is more open-ended than a mission statement. For example, Table 7.1 shows Amazon’s vision and mission statements. Notice how they differ.
| Amazon’s Vision Statement | Amazon’s Mission Statement |
|---|---|
| To be Earth’s most customer-centric company, where customers can find and discover anything they might want to buy online | We strive to offer our customers the lowest possible prices, the best available selection, and the utmost convenience |
Notice the differences in Amazon’s vision and mission statements. The vision statement is broader than the mission statement and looks to the future.
To create a strong vision statement, look at the broader field in which your organization operates. Be general. State a dream that is not currently attainable but that defines what your collective outcomes would be in a best-case scenario. Crafting a vision statement enables your organization, as a team, to identify key areas for potential growth and key social influences you can have, but it is important to stay focused on changes in your industry or sector as a general rule of thumb and to revisit your vision when those may warrant a change. For example, Netflix started out with the goal of providing optimum value and convenience for customers renting DVDs but as entertainment consumption platforms evolved it needed to adjust, and it has since shifted into streaming content for television. The company’s 2019 vision statement is “Becoming the best global entertainment distribution service.” 3
When crafting a vision statement, write questions beginning with, “How might we…?” or statements starting with, “In a perfect world, our organization would…” Craft a vision statement that hinges on the organization’s service goals and turns it into a lasting social good. (You should not promise to create world peace or give everybody a puppy, but you should look at how businesses operate in your field and dream of doing better strategically and socially.) These steps provide a good starting point:
- State how your organization would function in a dream scenario.
- Connect your organization’s dreams to broader hopes for progress.
- Define how you’re going to make the world a better place in the future through your products and services.
Dreams do not have to be wild to be broadly appealing or influential. The purpose of the vision statement is not to set unattainable goals but to open minds in the organization. If the vision statement has no grounding in reality, it can easily be written off; if it focuses on market share and product development (that is, tangible, mission-oriented things), the point is lost. Imagine your best team doing its best work with future capabilities and affordances made possible by other entrepreneurs and creators like you, and then state clearly what your influence as world changers could be. Again, the goal is not to develop unmanageable expectations or demand constant innovation from employees and contributors who have jobs that sustain day-to-day operations. The purpose is to develop a conversation about what is possible for the enterprise. For smaller startup enterprises (a deli or coffee shop, for example), the vision can be simpler but still focused on a unique experience they want to create for their customers. In other words, it should still be aspirational, with a link to the mission statement. Table 7.2 lists the vision statements of some companies across a variety of industries.
| Entity | Vision Statement |
|---|---|
| Alzheimer's Association | A world without Alzheimer’s disease |
| Teach for America | One day, all children in this nation will have the opportunity to attain an excellent education |
| Creative Commons | Realizing the full potential of the Internet—universal access to research and education, full participation in culture—to drive a new era of development, growth, and productivity |
| Warby Parker | To offer designer eyewear at a revolutionary price, while leading the way for socially conscious businesses |
| IKEA | To create a better everyday life for the many people |
Strong vision statements are forward-thinking.
A vision statement does not have to be long to be strong. One well-known vision statement contains only fifteen words: “At IKEA our vision is to create a better everyday life for the many people.” 4 This vision statement focuses on what IKEA hopes to accomplish, and what its employees can aspire to be—people who make everyday life better for others. Note the phrase “the many people.” This is purposeful: IKEA makes mass-marketed products and chooses to align its vision with its targeted consumers: many people. This vision statement is not framed as a political statement; rather, it is an ideal established for the global brand, and it indicates a broad positive outcome. IKEA’s statement is almost pure vision. A vision statement should connect an organization’s day-to-day work to a universal ideal rather than trying to draw a roadmap for implementation.
That being said, alongside its vision, the company follows up with what IKEA calls its “business idea.” It states: “Our business idea is ‘to offer a wide range of well-designed, functional home furnishing products at prices so low that as many people as possible will be able to afford them.’” This is something of a value proposition and a mission statement wrapped up in one. A value proposition explains what it is, exactly, that an organization or firm does that people will pay for (or contribute, to in the case of a nonprofit), and it is a central point in any pitch. We learned about value propositions in Identifying Entrepreneurial Opportunity as being integral to identifying opportunities, and you will learn how they figure into your business model in Business Model and Plan . But the discussion in this chapter is about how and why the value proposition needs to be articulated.
An example of a complicated vision statement is Coca-Cola’s. 5 While they are a very successful company, in the vision and mission statements published on their website, the distinctions between each can be difficult to discern. Figure 7.2 shows a large collection of statements and comments titled “Mission, Vision, & Values” on Coca-Cola’s website that includes sections on workplace culture, market focus, and “working smart.” These concepts, taken together, cover most of what is discussed in this section. Coca-Cola is not committing sins of omission with its “Mission, Vision, & Values” page. If anything, it tries to say too much. Also at issue is how these ideas are stated. For a company with massive global reach and some of the best, most memorable marketing moments, the relatively lifeless nature of its vision stands out.
This is a classic case of telling rather than showing . IKEA and Coca-Cola arguably have a similar vision. They want to make life a little bit better for people in an everyday way. But with this series of statements, Coca-Cola tries to cover all possible types of vision for almost every major relationship or facet of the corporation imaginable. Coca-Cola has a separate mission statement on its website, shown in Figure 7.3 .
While this is shared as a mission statement, it reads like a vision statement. The value proposition is relegated to an afterthought in convoluted corporate-speak. This is all tied into a vague “2020 Vision,” which is not truly a vision statement but appears more like a wrapper for the “Mission, Vision, & Values” content. 6 It is not clear what leadership, employees, business partners, or consumers are supposed to do with this information.
Coca-Cola is one of the world’s most recognizable brands. The company can grow by creating new products and by recapturing market share from competitors. It is essential, if and when Coca-Cola revises these statements, that it succinctly speak to all of those groups with one voice rather than trying to address each independently.
Can You Help Coca-Cola Rework Its “2020 Vision”?
Can you revise Coca-Cola’s vision statement so that it more clearly states how the corporation can be a force for good in the world? Read Coca-Cola’s “Mission, Vision, and Values” page then draft a new vision statement that alludes to hopes and potential accomplishments in the context of broad, positive, future outcomes for everyone the corporation comes into contact with.
Crafting a vision statement for an entrepreneurial endeavor is different from redrafting Coca-Cola’s vision statement. A startup is in the process of defining itself, which can make it challenging to establish a far-off vision, but crafting and adhering to a vision statement can remind leaders and employees what they are capable of and what their market is all about, so it is an important step. A good vision statement is sufficiently broad to allow for your organization to move within its marketplace while still aiming to do some good in the world.
Mission
In the chapter’s opening vignette, you learned about a young woman seeking to battle social injustice. Minkara’s mission was self-evident. It followed her experience facing prejudice in society. Other entrepreneurial missions may not be as personal or altruistic, but they can still be a force that drives passionate solution seeking. As we saw with Minkara, entrepreneurs often develop a product or service idea through a difficult or frustrating experience, whether a social injustice or a consumer frustration.
An entrepreneurial mission is a business or nonprofit organization’s reason for being. It is expressed as a self-conceptualization in the context of a marketplace and includes a sense of action. In considering a venture’s mission, relevant questions are: Who are we? What do we make or do? Why do we exist as an enterprise in the first place? Steve Jobs and Steve Wozniak, cofounders of Apple, had a mission to put personal computing in the hands of everyday consumers, which meant they had to create simple tools (a graphic user interface, mouse, and so on) in parallel with hardware.
A well-developed sense of mission establishes what an organization is and what it seeks to become. Even nonprofit organizations exist in marketplaces. They have to compete for resources and define themselves by the services they provide. Establishing a clear mission helps a nonprofit organization seek funding. It helps entrepreneurs in the for-profit world explain to investors, to customers, and to employees why their “thing,” whatever it is, is worth doing.
For example, the American Red Cross, one of the oldest and most well-known relief organization in the United States, has a very specific mission statement: “The American Red Cross prevents and alleviates human suffering in the face of emergencies by mobilizing the power of volunteers and the generosity of donors.” 7 Defining an organization’s mission clearly and specifically is essential for success.
A mission statement , as you read in the chapter on Identifying Entrepreneurial Opportunity is a clear expression of an organization’s reason for being that defines its primary long-term goal and often includes an abbreviated plan of action for how to reach that goal. A mission statement is written by answering these questions:
- Who are we?
- What do we make or do?
- Why do we exist as an enterprise?
Developing an effective mission statement and adhering to it puts members of an organization on the same page, and it communicates to potential partners and consumers that your organization knows where it is going. Mission statements can be revised, but it’s best to get it right at the start. A strong mission statement helps stakeholders prioritize the entity’s action steps and should guide decisions.
This Ted Talk from Simon Sinek is entitled “How Great Leaders Inspire Action.” Sinek is the author of two books: Start with Why and Leaders Eat Last.
When it comes to crafting an effective mission statement, clarity is key: It must be specific. What is left out of a mission statement is often as important as what is kept in. A good mission statement is focused, direct, and honest about the marketplace in question as well as the organization’s capabilities. It strikes the right balance between practicality and hope. For example, Patagonia, a well-known outdoor apparel company, has a compelling mission statement: “Patagonia: Build the best product, cause no unnecessary harm, use business to inspire and implement solutions to the environmental crisis.”
Check out this article on HubSpot about what makes an effective mission statement and tips on how to write them to learn more.
An inadequate mission statement might say this: “At Toys Inc., we make the best wooden toys money can buy, and our mission is to continue to grow to be a market leader in the classic toy industry.” A better mission statement might say this: “Toys Inc. is a market leader in North American wooden toy manufacturing. It is our mission to lead the global market in wooden puzzle and wooden toy car manufacturing and to serve customers with fresh versions of classic toys.” Both mission statements leave room for growth, but the second one defines more precisely what the organization is and where it is headed in the long term.
A mission statement should refrain from using clichés since these constrain the specific and unique vision of the venture. It should not limit innovation or creativity, and it should reference consumers or clients.
To create a strong mission statement, start by defining what the organization is. Even in a startup, you have a core problem-solution and an idea of what the product—and therefore the brand—will be. Be specific when defining your organization’s reason for being without limiting your avenues for growth. Include or embed the service mission within the broader mission. Again, the mission statement needs to do the following things with a tone of optimism:
- Define who you are.
- Define what you do now and for whom.
- Define what you want to do in the future.
In a startup, the mission may change substantially in the early phases. Mission statements should not be crafted in a way that limits an organization’s ability to pivot—that is, to adjust the value proposition to better achieve product-market fit (see the Launch for Growth to Success for a more in-depth discussion of pivoting). And while they should not be impervious to change, revise the mission statement only when it is necessary and helpful to do so. Companies and organizations usually change their mission statement when they have made a major shift (due to an acquisition, pivot to another market, new growth strategy, etc.) or if their purpose has changed in a major way.
For example, the March of Dimes organization was originally founded to serve people afflicted by polio, but with the success of polio vaccinations, the disease was eradicated in the United States. As a result, the March of Dimes changed its mission to focus on preventing birth defects, premature birth, and infant mortality. 8 In another example, Slack, a venture-backed startup that went public in mid-2019, was founded as a way for online game developers to collaborate. The original venture failed (twice), but the founder noticed that his engineers used the tool for rapid collaboration and did not need email or other functions of Microsoft Windows. Slack quickly communicated this change in a simple mission statement: “Slack is where work flows. It’s where the people you need, the information you share, and the tools you use come together to get things done.” 9
One thing should be clear: It is not the purpose of an organization to come up with better mission and vision statements. The purpose of an organization is to provide value to people and try to get paid or supported in doing so. The point of crafting mission and vision statements is to assist you to that end. Essentially, your vision statement is your dream, and your mission statement is your strategy in a real-world marketplace. The vision is a statement about why you matter as an organization with a view of what the organization will become in the future, while the mission is a statement about those who might be served by the venture. Refining these statements will help you clarify your entrepreneurial story.
Goals
An organization needs to establish concrete goals for its products and services to remain viable. Goals should be stated in precise terms that are appropriate for the marketplace. For example, a new “white table” Italian restaurant in Chicago needs an initial goal on how it will attract and retain new customers based on its vision and mission, relative to what is already available. A new company’s initial goal is probably not to crush all competition and take over a monopoly position. Instead, it may hope to capture a percentage of a close competitor’s market share or create a new product to reach a niche market. In those instances, goals would be stated as specific outcomes to attract competitors’ customers, or in the case of a niche business (like Spanx), to define a new category of women’s comfort apparel. Lululemon Athletica, which pioneered customer-centered designs for women’s athletic apparel, recently established new growth goals that were consistent with its mission: “Management is hard set on growing the company to $4 billion in revenue by 2020. This involves growing historically small contributors to the top line, such as men’s, international, and the digital business.” 10
Goals can be tactical in the short term too. They should be reasonable, influenced by a detailed understanding of the marketplace and the competition, and attainable. Nothing stunts growth and clouds the path to achieving your vision more quickly than setting unattainable goals and holding members of an organization to impossible standards. Instead, set SMART goals, which you first were introduced to in The Entrepreneurial Perspective . SMART stands for specific, measurable, achievable, relevant, and timely. The best goals clearly communicate all of these elements, as shown in Figure 7.4 .
To break these down, SMART goals should be:
- Specific: Your goals should be precise rather than overly broad.
- Measurable: You should be able to test, in some quantifiable manner, whether a goal has been met, meaning that there needs to be some method to determine whether the goal has been met.
- Achievable: The goal must be attainable; it cannot be so lofty that it cannot be accomplished. On the other hand, the goal should not be so easy that it can be accomplished quickly or with little effort.
- Relevant: The goal should be well suited for what you want to accomplish; this means that the goal should be relevant to the outcome needed.
- Timely: Each goal needs to have a defined deadline: the time when the goal must be accomplished. What time frame do you have for completing your goals? How does this timeline fit into your overall plan?
Is it a reasonable goal for a specialty soap company to strive to capture 1.5 percent of the global market share two years after incorporating? Let’s deconstruct the goal to assess how SMART it is. It is specific because it establishes a clearly targeted amount (1.5 percent) of a defined market (global specialty soaps). Market share is measurable . We can assume that this is an attainable goal for our imaginary startup. Is it relevant? Capturing market share is always relevant because it translates to near-term earnings and potential for future earnings at the same time. The goal as stated is also timely (within two years). Thus, this is a SMART goal.
Check out the University of Virginia’s detailed exercise on writing SMART goals to learn more. It includes one example of a SMART goal, and, for each letter, it includes an explanation of how the concept is applied. Follow the link to write your own SMART goal and analyze it using a helpful questionnaire. 11
SMART goals are not guarantees of success. As an entrepreneur, you could be wrong about whether a goal is attainable, for example. Or you may fail at measuring outcomes correctly, and your idea may not be as well defined or unique as you thought. Nevertheless, it is much better to set goals with all of these factors in mind than to practice wishful thinking or set abstract goals and hope to reach business benchmarks by luck.
SMART Goals for Social Activism
You can use SMART goal-setting methods to plan a peaceful social demonstration. Mobilizing people to speak out about an issue that they want political leaders to address is one of the most basic tasks social entrepreneurs undertake. Social entrepreneurs who go on to found successful nonprofit organizations often cut their teeth in this kind of base-level activism. But just because the concepts underlying demonstrating are somewhat straightforward—contact media, gather people, march, demonstrate, speak out, tell your story, clearly state your petition for change (also known as a “redress of grievances”), peacefully disperse, and strategize next steps—that does not mean that the process is always done according to SMART tactics. Protest organizers often vary immensely in their organizing skills.
Here is the task: Think of an issue that you want addressed on your campus or in your community. Define it and draft a plan for a peaceful demonstration wherein the demonstration is clearly goal-oriented.
- State the specific issue you want addressed, who you want to address it, and what you want them to do.
- State several ways you might measure the success of your protest. Are you seeking media awareness, legislative change, or specific action regarding an individual victim or perpetrator of a crime? Be sure to clearly state not only reasonable expectations regarding reactions to your demonstration but also measurable outcomes you can communicate to others as you work to gather interest in your cause.
- Note whether your demands target the right leaders and whether what you ask of them is something you can attain.
- Demonstrate clearly how the specific action you plan to take is relevant to the cause at hand. Will you demonstrate in one place? Will you carry out some form of active protest such as a “die-in” at a certain location? 12 Will you practice nonviolent civil disobedience? Clearly explain why your action is relevant to your requests or demands. If you are planning an act of peaceful civil disobedience, are you and everyone you are encouraging to participate aware of the possible consequences, such as arrest? If someone is risking arrest to help demonstrate for an important cause, they are right to demand of protest organizers that the action be relevant and easy for target audiences to understand.
- Is your strategy timely? Are you planning a demonstration with measurable outcomes that will occur according to a timeframe you can track? It is generally ill-advised to petition for general fixes to complex solutions without paying attention to existing legislative and/or communicative cycles.
Note that this is presented as an exercise only. Much more planning goes into successful demonstrations, but this should give you a sense of how SMART goal setting can be useful for social entrepreneurship. It is not only for taking business risks. You can use SMART tactics to peacefully push for important changes. Recognize, obviously, that the risks are quite different for this type of social entrepreneurship than for other types of endeavors.
Thinking like a business entrepreneur again, recognize that SMART goal setting is a tactic for getting things done in the short term. You can line up several attainable goals over a period of several weeks or months, and build your way to a complex, realistic business plan. The Small Business Administration (SBA) business plan template, 13 for example, includes eleven core sections and, as a blank outline, is thirty-five pages long. If you set a SMART goal to complete each section in about a week, in three months, you would have a comprehensive business plan.


16.1: Introduction to Biotechnology and Genomics
The study of nucleic acids began with the discovery of DNA, progressed to the study of genes and small fragments, and has now exploded to the field of genomics. Genomics is the study of entire genomes, including the complete set of genes, their nucleotide sequence and organization, and their interactions within a species and with other species. The advances in genomics have been made possible by DNA sequencing technology. Just as information technology has led to Google maps that enable people to get detailed information about locations around the globe, genomic information is used to create similar maps of the DNA of different organisms. These findings have helped anthropologists to better understand human migration and have aided the field of medicine through the mapping of human genetic diseases. The ways in which genomic information can contribute to scientific understanding are varied and quickly growing.
Contributors and Attributions
-
Connie Rye (East Mississippi Community College), Robert Wise (University of Wisconsin, Oshkosh), Vladimir Jurukovski (Suffolk County Community College), Jean DeSaix (University of North Carolina at Chapel Hill), Jung Choi (Georgia Institute of Technology), Yael Avissar (Rhode Island College) among other contributing authors. Original content by OpenStax (CC BY 4.0; Download for free at<EMAIL_ADDRESS>).


Describe sexuality and fertility issues related to early adulthood
Sexual Responsiveness and Reproduction in Early Adulthood
Sexual Responsiveness
Men and women tend to reach their peak of sexual responsiveness at different ages. For men, sexual responsiveness tends to peak in the late teens and early twenties
.
Sexual arousal can easily occur in response to physical stimulation or fantasizing. Sexual responsiveness begins a slow decline in the late twenties and into the thirties although a man may continue to be sexually active throughout adulthood. Over time, a man may require more intense stimulation in order to become aroused. Women often find that they become more sexually responsive throughout their 20s and 30s and may peak in the late 30s or early 40s. This is likely due to greater self-confidence and reduced inhibitions about sexuality.
 For example, among emerging adults in the United States, it is common for oral sex to not be considered “real sex.. In the 1950s and 1960s, about 75 percent of people between the ages of 20–24 engaged in premarital sex; today, that number is 90 percent. Unintended pregnancy and sexually transmitted infections and diseases (STIs/STDs) are a central issue. As individuals move through emerging adulthood, they are more likely to engage in monogamous sexual relationships and practice safe sex.
Reproduction
For many couples, early adulthood is the time for having children. However, delaying childbearing until the late 20s or early 30s has become more common in the United States. The mean age of first-time mothers in the United States increased 1.4 years, from 24.9 in 2000 to 26.3 in 2014. This shift can primarily be attributed to a larger number of first births to older women along with fewer births to mothers under age 20 (CDC, 2016).
[1]
Couples delay childbearing for a number of reasons. Women are now more likely to attend college and begin careers before starting families. And both men and women are delaying marriage until they are in their late 20s and early 30s. In 2018, the average age for a first marriage in the United States was 29.8 for men and 27.8 for women.
[2]
Infertility
Infertility affects about 6.7 million women or 11 percent of the reproductive age population (American Society of Reproductive Medicine [ASRM], 2006-2010. Male factors create infertility in about a third of the cases. For men, the most common cause is a lack of sperm production or low sperm production. Female factors cause infertility in another third of cases. For women, one of the most common causes of infertility is ovulation disorder. Other causes of female infertility include blocked fallopian tubes, which can occur when a woman has had
pelvic inflammatory disease (PID)
or
endometriosis
. PID is experienced by 1 out of 7 women in the United States and leads to infertility about 20 percent of the time. One of the major causes of PID is
Chlamydia
, the most commonly diagnosed sexually transmitted infection in young women. Another cause of pelvic inflammatory disease is
gonorrhea
. Both male and female factors contribute to the remainder of cases of infertility and approximately 20 percent are unexplained.
Watch It
Watch this video to learn more about the reasons for infertility and the main treatment methods available for conceiving.
A link to an interactive elements can be found at the bottom of this page.
The majority of infertility cases (85-90 percent) are treated using fertility drugs to increase ovulation or with surgical procedures to repair the reproductive organs or remove scar tissue from the reproductive tract.
In vitro fertilization (IVF)
is used to treat infertility in less than 5 percent of case
s. IVF is used when a woman has blocked or deformed fallopian tubes or sometimes when a man has a very low sperm count. This procedure involves removing eggs from the female and fertilizing the eggs outside the woman’s body. The fertilized egg is then reinserted in the woman’s uterus. The average cost of an IVF cycle in the U.S. is $10,000-15,000 and the average live delivery rate for IVF in 2005 was 31.6 percent per retrieval. IVF makes up about 99 percent of artificial reproductive procedures. [ASRM, 2006-2010]
Less common procedures include
gamete intrafallopian tube transfer (GIFT)
which involves implanting both sperm and ova into the fallopian tube and fertilization is allowed to occur naturally.
Zygote intrafallopian tube transfer (ZIFT)
is another procedure in which sperm and ova are fertilized outside of the woman’s body and the fertilized egg or zygote is then implanted in the fallopian tube. This allows the zygote to travel down the fallopian tube and embed in the lining of the uterus naturally.
Insurance coverage for infertility is required in fourteen states, but the amount and type of coverage available vary greatly (ASRM, 2006-2010). The majority of couples seeking treatment for infertility pay much of the cost. Consequently, infertility treatment is much more accessible to couples with higher incomes. However, grants and funding sour
ces may be available
for lower-income couples seeking infertility treatment.
Fertility for Singles and Same-Sex Couples
The journey to parenthood may look different for singles same-sex couples. However, there are several viable options available to them to have their own biological children. Men and women may choose to donate their sperm or eggs to help others reproduce for monetary or humanitarian reasons.  One or both of the men would provide the sperm and choose a carrier. The chosen woman may be the source of the egg and uterus or the woman could be a third party that carries the created embryo.
Reciprocal IVF is used by couples who both possess female reproductive organs. Using in vitro fertilization, eggs are removed from one partner to be used to make embryos that the other partner will hopefully carry in a successful pregnancy.
Artificial insemination
(
AI
) is the deliberate introduction of sperm into a female’s cervix or uterine cavity for the purpose of achieving a pregnancy through in vivo fertilization by means other than sexual intercourse. AI is most often used by single women who desire to give birth to their own child, women who are in a lesbian relationship, or women who are in a heterosexual relationship but with a male partner who is infertile or who has a physical impairment which prevents intercourse. The sperm used could be anonymous or from a known donor.
the deliberate introduction of sperm into a female’s cervix in order to become pregnant by means other than sexual intercourse
chlamydia
a sexually transmitted infection caused by the bacterium chlamydia trachomatis
endometriosis
a condition in which the layer of tissue that normally covers the inside of the uterus, grows outside of it
gamete intrafallopian tube transfer
involves implanting both sperm and ova into the fallopian tube which allows fertilization to occur naturally
gonorrhea
a sexually transmitted infection (STI) caused by the bacterium neisseria gonorrhoeae
in vitro fertilization
this procedure involves removing eggs from the female, fertilizing the eggs outside the woman’s body, and then reinserting into the woman’s uterus
pelvic inflammatory disease
an infection of the upper part of the female reproductive system, namely the uterus, fallopian tubes, and ovaries, and inside of the pelvis
zygote intrafallopian tube transfer
sperm and ova are fertilized outside of the woman’s body and the zygote is then implanted in the fallopian tube to allow the zygote to travel and embed in the lining of the uterus naturally
Modification, adaptation, and original content.
Authored by
: Margaret Clark-Plaskie for Lumen Learning.
Provided by
: Lumen Learning.
License
:
CC BY: Attribution


3.6: Resonance
In the previous section, we constructed a Lewis diagram for the carbonate anion. Our final structure showed two carbon-oxygen single bonds and one carbon-oxygen double bond. The structure that we drew is shown below, along with two other possible representations for the carbonate anion. These structures differ only in the position of the carbon-oxygen double bond.
So which of these is correct? Actually, they all are! These are all “proper” Lewis diagrams for a covalent structure having constant geometry, and the diagrams differ only in the manner that we have arbitrarily arranged the electrons. These Lewis diagrams are called resonance forms . For the carbonate anion, there are three equivalent resonance forms that can be drawn. It is important to note that the electrons are not “hopping” between the atoms, but that the electrons are spread evenly between the carbon and all three oxygens and that each carbon-oxygen bond has a bond-order of 1.33 (one and one-third covalent bonds). A structure such as this is called the resonance hybrid , and although it most clearly represents the actual bonding in the compound, it is often difficult to understand the nature of the bonding when structures are represented as resonance hybrids. A full discussion of resonance is beyond the scope of an introductory text and, for structures such as the carbonate anion, we will accept any of the proper resonance forms shown above.


27.1: Introduction to the Thyroid and Parathyroid
By the end of this section, you should be able to:
- 27.1.1 Describe the function of the thyroid and parathyroid glands.
- 27.1.2 Discuss hormones associated with the thyroid and parathyroid glands.
Thyroid and Parathyroid Glands
The thyroid gland is a butterfly-shaped gland located at the front of the neck below the voice box (see Figure 27.2). This important gland regulates metabolism in the body through the production and secretion of thyroid hormones, which require iodine for synthesis. The thyroid gland produces the active thyroid hormone, triiodothyronine (T3) , and the inactive thyroid hormone, thyroxine (T4) . Thyroid follicular cells secrete T3 and T4, while parafollicular cells secrete calcitonin cells that aid calcium metabolism. Follicular cells line the follicles, which are small spherical structures in the thyroid gland. They absorb iodine from the blood and combine it with T3 and T4. Parafollicular cells are scattered between the follicles of the thyroid gland. Their main function is to secrete calcitonin for calcium regulation. Calcitonin lowers the levels of calcium in the blood by inhibiting the activity of osteoclasts—cells that break down bone tissue and release calcium into the blood. When calcium levels in the blood rise, the thyroid gland releases calcitonin, which binds to receptors on the surface of osteoclasts and inhibits their activity, reducing the amount of calcium released from the bone into the blood, thereby lowering calcium levels in the blood (McLaughlin & Jialal, 2022).
Link to Learning
Diagnostic Testing
Diagnostic testing is key in determining thyroid and parathyroid conditions. Review the article Thyroid Function Testing in the Diagnosis and Monitoring of Thyroid Function Disorder. The first figure in the article illustrates an algorithm commonly used when diagnosing thyroid and parathyroid disorders.
Other diagnostic tests that assist in diagnosing thyroid and parathyroid conditions include:
- Ionized serum calcium: This test is performed for conditions that affect the body’s ability to balance the amounts of ionized calcium and bound calcium in the blood. The normal range is 1.12–1.23 mmol/L, although ranges may vary slightly depending on the laboratory (American Board of Internal Medicine, 2023).
- Vitamin D (calciferol): This test is performed to determine the amount of vitamin D in the blood, which helps the body to absorb calcium. The normal range is 30–60 ng/mL, although ranges may vary slightly depending on the laboratory (American Board of Internal Medicine, 2023).


12.5: Boundaries at Work
Setting—and Crossing—Boundaries
Boundaries can be used as “gateways” into different domains of our lives (Matthews, et al., 2010) that create “physical, temporal, emotional, cognitive, and/or relational limits” (Ashforth, et al., 2000, p. 474). That is, we create boundaries to funnel behaviors and/or actions that we allow in or not, based on the person, location, context, and more in our relationships with others. Setting boundaries can be challenging, as boundaries are defined as “the never-ending, hands-on, largely visible process through which boundaries are negotiated, placed, maintained, and transformed by individuals over time” (Nippert-Eng, 1996, xiii). Trefalt (2013) argues that boundaries are a fundamentally relational process, and that you cannot neglect the relational context of boundaries, as the past, consequences, and experiences as those involved must be factored into the equation. In this section, we will briefly cover examples where boundaries were crossed in the workplace.
Interpersonal relationships at work sometimes cross boundaries. We want to acknowledge that building mutual interpersonal relationships at your workplace does not include taking part in harassment of any kind, stereotyping others, or otherwise violating the explicit boundaries of others. We also would like to provide some context as to how common some harmful interpersonal communication exchanges are in our workspaces, hoping to shed light on how to sight and identify and then, hopefully, eliminate them from your interpersonal exchanges (US Equal Employment Opportunity Commission, 2021).
Harassment and Biases
As we discussed earlier in this chapter, mutual workplace relationships are common. However, there are instances when workplace relationships occur that are very much one-sided, unwelcome, and unwanted by the receiving party. Here, we will focus on interpersonal communication patterns of harassment and biases in the workplace.
To learn more about biases, check out diversity advocate Vernā Myers’ TED Talk: How to overcome our biases? Walk boldly toward them . You may also read the transcript . According to Myers, we can learn how to examine our subconscious attitudes toward out-groups and then move toward, not away from, those that make us feel uncomfortable.
It is helpful to understand the definitions of harassment and bias. For our purposes. harassment is defined by Cornell Law School as
offensive, unwelcome conduct based on the victim's protected characteristic, that is so severe or pervasive that it affects the terms and conditions of the victim's employment. Harassment may take the form of words, actions, gestures, demands, or visual displays, such as photographs or cartoons. (Legal Information Institute, 2021, para. 1)
This can be present across interpersonal relationships at work. According to the U.S. Equal Opportunity Commission (2021) the harasser can be “the victim's supervisor, a supervisor in another area, an agent of the employer, a co-worker, or a non-employee” and “the victim does not have to be the person harassed but can be anyone affected by the offensive conduct” (para. 6).
Bias has more nuanced definitions: explicit bases are understood as overt prejudices and attitudes about a group, like racism or misogyny, while unconscious and implicit biases are deeply held beliefs about others that may unconsciously drive attitudes and behavior (Rimnac, 2020). These exchanges can manifest in the form of verbal and nonverbal actions directed towards others (Bouckenooghe, et al. 2015).
Harassment and biases can take many forms; in this section we just scratch the surface of some of the most reported and researched facets of these areas.
Sexual Harassment in the Workplace
The US Equal Employment Opportunities Commission defines sexual harassment as
unwelcome sexual advances, request for sexual favors, and other verbal or physical harassment of a sexual nature constitutes sexual harassment when this conduct explicitly or implicitly affects an individual’s employment, unreasonably interferes with an individual’s work performance, or creates an intimidating, hostile, or offensive work environment. (2021)
Given this definition, have you ever felt harassed at work? Did you say something? Did you ignore it? Did you make an official report?
In 2020 the US Equal Employment Opportunity Commission received 6,587 sexual harassment claims. Of those claims, 16.8% were made by men (US Equal Employment Opportunity Commission, 2021). Research finds that men are the most common perpetrators of sexual harassment. Although men do harass other men, women are the most common targets (Cortina & Berdahl, 2008).  Brassel (2020) found that this pattern may be caused by the masculine structures and hierarchy present in Western culture.
Sexual harassment causes problems within an organization by lowering the quality of the organizational lives of female employees and creating obstacles that prevent employees from fully engaging with their organization (McDonald et al., 2011). Additionally, studies argue that sexual harassment creates professional, psychological, and physical health problems for those involved (National Academies of Sciences, Engineering, and Medicine, 2018). Statistics also suggest that “only a small number of those who experience harassment (one in ten) ever formally report”—and the most common reason for this silence is for fear of retaliation (Shaw, et al., 2018, p. 2).
Racial and Gender Biases
Although biases are not as obvious as harassment, we know that they are rampant across the workspace, from large to small organizations, from executives to entry-level employees, and in both private and public sectors (Bielby, 2000). Athough biases can target any facet of another’s identity, we will focus on racial and gender bias . Researchers have struggled to determine how harmful or costly biases are because they are hard to measure. Though some gender bias, like harassment, has been measured and studied, more subtle gender bias barriers, like the "glass cliff," when women are placed in positions of power while things are going poorly, other biases may not be recognized, obvious, or even called out (Stuart, 2018). We know from surveying the research that biases in the workplace impact the way we communicate with others.
In gender-bias research by Glass and Cook (2016) 97% of respondents said they worry about how they come off to others when exercising authority, 87% downplay their accomplishments to others, and 66% make less money than their male counterparts. Research has found that companies without women in top leadership roles can hurt their sales and profitability (Glass & Cook, 2016).
So how can we help combat interpersonal communication patterns of harassment and bias? First, we need to recognize them and acknowledge them in our place of work. Next, we can report them through the proper channels. Per most HR policy violations, sexual harassment can be reported by those who are not the victim of the harassment (EEOC, 2021). And lastly, we can help prevent or mitigate them from happening in the first place.
An individual can become more self-aware of our own implicit biases through tools like the Harvard IATs . We can also sign up for and engage in professional development opportunities that talk about such matters.  And with implicit and unconscious bias gaining some traction, many organizations are bringing in guest speakers, or even consultants, to address common issues in our workplace.


Chapter 14
One example for NH 3 as a conjugate acid: as a conjugate base:
(a) (b) (c) (d) (e) (f)
(a) (b) (c) (d) (e) (f)
(a) H 2 O, O 2− ; (b) H 3 O + , OH − ; (c) H 2 CO 3 , (d) (e) H 2 SO 4 , (f) (g) H 2 S; S 2− ; (h) H 4 N 2
The labels are Brønsted-Lowry acid = BA; its conjugate base = CB; Brønsted-Lowry base = BB; its conjugate acid = CA. (a) HNO 3 (BA), H 2 O(BB), H 3 O + (CA), (b) CN − (BB), H 2 O(BA), HCN(CA), OH − (CB); (c) H 2 SO 4 (BA), Cl − (BB), HCl(CA), (d) OH − (BB), (CB), H 2 O(CA); (e) O 2− (BB), H 2 O(BA) OH − (CB and CA); (f) [Cu(H 2 O) 3 (OH)] + (BB), [Al(H 2 O) 6 ] 3+ (BA), [Cu(H 2 O) 4 ] 2+ (CA), [Al(H 2 O) 5 (OH)] 2+ (CB); (g) H 2 S(BA), HS − (CB), NH 3 (CA)
Amphiprotic species may either gain or lose a proton in a chemical reaction, thus acting as a base or an acid. An example is H 2 O. As an acid: As a base:
amphiprotic: (a) (b) not amphiprotic: (c) Br − ; (d) (e)
In a neutral solution [H 3 O + ] = [OH − ]. At 40 °C, [H 3 O + ] = [OH − ] = (2.910 × 10 −14 ) 1/2 = 1.7 10 −7 .
x = 3.051 10 −7 M = [H 3 O + ] = [OH − ]; pH = −log3.051 10 −7 = −(−6.5156) = 6.5156; pOH = pH = 6.5156
(a) pH = 3.587; pOH = 10.413; (b) pOH = 0.68; pH = 13.32; (c) pOH = 3.85; pH = 10.15; (d) pOH = −0.40; pH = 14.4
[H 3 O + ] = 3.0 10 −7 M ; [OH − ] = 3.3 10 −8 M
[H 3 O + ] = 1 10 −2 M ; [OH − ] = 1 10 −12 M
[OH − ] = 3.1 10 −12 M
The salt ionizes in solution, but the anion slightly reacts with water to form the weak acid. This reaction also forms OH − , which causes the solution to be basic.
[H 2 O] > [CH 3 CO 2 H] > ≈ > [OH − ]
The oxidation state of the sulfur in H 2 SO 4 is greater than the oxidation state of the sulfur in H 2 SO 3 .
The stronger base or stronger acid is the one with the larger K b or K a , respectively. In these two examples, they are (CH 3 ) 2 NH and
triethylamine
(a) higher electronegativity of the central ion. (b) H 2 O; NH 3 is a base and water is neutral, or decide on the basis of K a values. (c) HI; PH 3 is weaker than HCl; HCl is weaker than HI. Thus, PH 3 is weaker than HI. (d) PH 3 ; in binary compounds of hydrogen with nonmetals, the acidity increases for the element lower in a group. (e) HBr; in a period, the acidity increases from left to right; in a group, it increases from top to bottom. Br is to the left and below S, so HBr is the stronger acid.
(a) NaHSeO 3 < NaHSO 3 < NaHSO 4 ; in polyoxy acids, the more electronegative central element—S, in this case—forms the stronger acid. The larger number of oxygen atoms on the central atom (giving it a higher oxidation state) also creates a greater release of hydrogen atoms, resulting in a stronger acid. As a salt, the acidity increases in the same manner. (b) the basicity of the anions in a series of acids will be the opposite of the acidity in their oxyacids. The acidity increases as the electronegativity of the central atom increases. Cl is more electronegative than Br, and I is the least electronegative of the three. (c) HOI < HOBr < HOCl; in a series of the same form of oxyacids, the acidity increases as the electronegativity of the central atom increases. Cl is more electronegative than Br, and I is the least electronegative of the three. (d) HOCl < HOClO < HOClO 2 < HOClO 3 ; in a series of oxyacids of the same central element, the acidity increases as the number of oxygen atoms increases (or as the oxidation state of the central atom increases). (e) and are anions of weak bases, so they act as strong bases toward H + . and HS − are anions of weak acids, so they have less basic character. In a periodic group, the more electronegative element has the more basic anion. (f) with a larger number of oxygen atoms (that is, as the oxidation state of the central ion increases), the corresponding acid becomes more acidic and the anion consequently less basic.
1. Assume that the change in initial concentration of the acid as the equilibrium is established can be neglected, so this concentration can be assumed constant and equal to the initial value of the total acid concentration. 2. Assume we can neglect the contribution of water to the equilibrium concentration of H 3 O + .
(b) The addition of HCl
(a) Adding HCl will add H 3 O + ions, which will then react with the OH − ions, lowering their concentration. The equilibrium will shift to the right, increasing the concentration of HNO 2 , and decreasing the concentration of ions. (b) Adding HNO 2 increases the concentration of HNO 2 and shifts the equilibrium to the left, increasing the concentration of ions and decreasing the concentration of OH − ions. (c) Adding NaOH adds OH − ions, which shifts the equilibrium to the left, increasing the concentration of ions and decreasing the concentrations of HNO 2 . (d) Adding NaCl has no effect on the concentrations of the ions. (e) Adding KNO 2 adds ions and shifts the equilibrium to the right, increasing the HNO 2 and OH − ion concentrations.
This is a case in which the solution contains a mixture of acids of different ionization strengths. In solution, the HCO 2 H exists primarily as HCO 2 H molecules because the ionization of the weak acid is suppressed by the strong acid. Therefore, the HCO 2 H contributes a negligible amount of hydronium ions to the solution. The stronger acid, HCl, is the dominant producer of hydronium ions because it is completely ionized. In such a solution, the stronger acid determines the concentration of hydronium ions, and the ionization of the weaker acid is fixed by the [H 3 O + ] produced by the stronger acid.
(a) (b) (c) (d)
(a) (b) (c) (d) (e) (f)
(a)
Solving for
x
gives 1.63 10
−5
M
. This value is less than 5% of 0.0092, so the assumption that it can be neglected is valid. Thus, the concentrations of solute species at equilibrium are:
[H
3
O
+
] = [ClO
–
] = 1.6 10
−5
M
[HClO
–
] = 0.0092
M
[OH
−
] = 6.1 10
−10
M
;
(b)
Solving for
x
gives 5.81 10
−6
M
. This value is less than 5% of 0.0784, so the assumption that it can be neglected is valid. Thus, the concentrations of solute species at equilibrium are:
= [OH
−
] = 5.8 10
−6
M
[C
6
H
5
NH
2
] = 0.0784
M
[H
3
O
+
] = 1.7 10
−9
M
;
(c)
Solving for
x
gives 6.30 10
−6
M
. This value is less than 5% of 0.0810, so the assumption that it can be neglected is valid. Thus, the concentrations of solute species at equilibrium are:
[H
3
O
+
] = [CN
−
] = 6.3 10
−6
M
[HCN] = 0.0810
M
[OH
−
] = 1.6 10
−9
M
;
(d)
Solving for
x
gives 2.63 10
−3
M
. This value is less than 5% of 0.11, so the assumption that it can be neglected is valid. Thus, the concentrations of solute species at equilibrium are:
[(CH
3
)
3
NH
+
] = [OH
−
] = 2.6 10
−3
M
[(CH
3
)
3
N] = 0.11
M
[H
3
O
+
] = 3.8 10
−12
M
;
(e)
Solving for
x
gives 1.39 10
−4
M
. This value is less than 5% of 0.120, so the assumption that it can be neglected is valid. Thus, the concentrations of solute species at equilibrium are:
[Fe(H
2
O)
5
(OH)
+
] = [H
3
O
+
] = 1.4 10
−4
M
= 0.120
M
[OH
−
] = 7.2 10
−11
M
pH = 2.41
[C 10 H 14 N 2 ] = 0.049 M ; [C 10 H 14 N 2 H + ] = 1.9 10 −4 M ; = 1.4 10 −11 M ; [OH − ] = 1.9 10 −4 M ; [H 3 O + ] = 5.3 10 −11 M
(a) acidic; (b) basic; (c) acidic; (d) neutral
[H 3 O + ] and are practically equal
[C 6 H 4 (CO 2 H) 2 ] 7.2 10 −3 M , [C 6 H 4 (CO 2 H)(CO 2 ) − ] = [H 3 O + ] 2.8 10 −3 M , 3.9 10 −6 M , [OH − ] 3.6 10 −12 M
(a)
(b)
(c)
Solving for
x
gives 1.5 10
−11
M
. Therefore, compared with 0.014
M
, this value is negligible (1.1 10
−7
%).
Excess H
3
O
+
is removed primarily by the reaction:
Excess base is removed by the reaction:
[H 3 O + ] = 1.5 10 −4 M
[OH − ] = 4.2 10 −4 M
(a) The added HCl will increase the concentration of H 3 O + slightly, which will react with and produce CH 3 CO 2 H in the process. Thus, decreases and [CH 3 CO 2 H] increases. (b) The added KCH 3 CO 2 will increase the concentration of which will react with H 3 O + and produce CH 3 CO 2 H in the process. Thus, [H 3 O + ] decreases slightly and [CH 3 CO 2 H] increases. (c) The added NaCl will have no effect on the concentration of the ions. (d) The added KOH will produce OH − ions, which will react with the H 3 O + , thus reducing [H 3 O + ]. Some additional CH 3 CO 2 H will dissociate, producing ions in the process. Thus, [CH 3 CO 2 H] decreases slightly and increases. (e) The added CH 3 CO 2 H will increase its concentration, causing more of it to dissociate and producing more and H 3 O + in the process. Thus, [H 3 O + ] increases slightly and increases.
pH = 8.95
37 g (0.27 mol)
(a) pH = 5.222; (b) The solution is acidic. (c) pH = 5.220
At the equivalence point in the titration of a weak base with a strong acid, the resulting solution is slightly acidic due to the presence of the conjugate acid. Thus, pick an indicator that changes color in the acidic range and brackets the pH at the equivalence point. Methyl orange is a good example.
(a) pH = 2.50; (b) pH = 4.01; (c) pH = 5.60; (d) pH = 8.35; (e) pH = 11.08


11.13: Putting It Together- Communicating Different Messages
As we have discussed in this module, business communication is an exercise in problem solving. The strategy for creating and delivering professional written messages calls for a thoughtful approach to the situation at hand, going beyond simply what you want to say.
We explored the prevalence of informative messages in the workplace. An informative message in the workplace is simply the sharing of meaningful information among people in an unbiased and professional manner. Informative messages can be short or long, formal or casual in tone, internal or external in focus, and direct or indirect in structure depending on the situation. Like all forms of communication, the purpose of informative messages is to promote understanding, encourage action, stimulate thinking, or promote ideas.
We listed the following guidelines for creating informative messages:
- Get to the main idea as quickly as possible.
- Use a greeting to identify the audience.
- Be clear and concise with the presentation of information.
- Check your message for grammatical errors.
- Include a call to action.
For short informative messages, we discussed using IM and Twitter as delivery possibilities. For longer informative messages, we explored the use of email, blog, presentation and podcasts.
Our discussion then turned to team-focused communication. We started by stating the importance of collaborative teams in the workplace. Successful teams are the key to productivity in business today, and team-focused communication was shown to be a key ingredient in creating the proper atmosphere for building and supporting team-based workplaces. We then explored the many options for team-focused written messages and discussed the pros and cons of several of them. At the end of the day we came to the conclusion that team collaboration software platforms are probably the best answer.
Critical messages make up another large segment of communication in business. We discussed several likely scenarios: a critical message to a non-related company, a critical message to a customer, a critical message to a subordinate and a critical message to a colleague. Going back to our thoughtful strategies based on circumstances, we demonstrated how the direct versus indirect style, the constructive style and active versus passive voice style could be used for each scenario.
Finally we explored written responses to criticism. We noticed that this topic involved our behavior as much as our expertise when the criticism was incoming. We discussed ways to remain professional despite frustration and other workplace issues. And we discussed guidelines and recommendations for written responses to external and internal criticism. Even the best corporate culture will see conflict arise from within and without. The tools in this module will be invaluable in dealing with them.
Contributors and Attributions
- Putting It Together. Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution


2.29: Introduction to Describing a Distribution
What you’ll learn to do: Describe a distribution using mean and standard deviation
As important as proper study design, clearly representing data is a fundamental part of a good statistical analysis. In describing a distribution based on quantitative data, we present both numerical and graphical summaries. Putting our previous sections together, we first begin by visually representing the data in a dotplot or histogram. Based on the shape, skew, and outliers, appropriate measures of center and spread help us further understand the distribution.
Contributors and Attributions
CC licensed content, Shared previously
- Concepts in Statistics. Provided by : Open Learning Initiative. Located at : http://oli.cmu.edu . License : CC BY: Attribution


6.2.4: Different Options for Solving One Equation
Lesson
Let's think about which way is easier when we solve equations with parentheses.
Exercise \(\PageIndex{1}\): Algebra Talk: Solve Each Equation
\(100(x-3)=1,000\)
\(500(x-3)=5,000\)
\(0.03(x-3)=0.3\)
\(0.72(x+2)=7.2\)
Exercise \(\PageIndex{2}\): Analyzing Solution Methods
Three students each attempted to solve the equation \(2(x-9)=10\), but got different solutions. Here are their methods. Do you agree with any of their methods, and why?
Noah’s method:
\(\begin{aligned} 2(x-9)&=10 \\ 2(x-9)+9&=10+9\qquad\text{ add }9\text{ to each side} \\ 2x&=19 \\ 2x\div 2&=19\div 2\qquad\text{ divide each side by }2 \\ x&=\frac{19}{2}\end{aligned}\)
Elena's method:
\(\begin{aligned} 2(x-9)&=10 \\ 2x-18&=10 \qquad\text{ apply the distributive property} \\ 2x-18-18&=10-18\qquad\text{ subtract }18\text{ from each side} \\ 2x&=-8 \\ 2x\div 2&=-8\div 2 \qquad\text{ divide each side by }2 \\ x&=-4\end{aligned}\)
Andre's method:
\(\begin{aligned} 2(x-9)&=10 \\ 2x-18&=10 \qquad \text{ apply the distributive property} \\ 2x-18+18&=10+18 \qquad\text{ add }18\text{ to each side} \\ 2x&=28 \\ 2x\div 2&=28\div 2\qquad\text{ divide each side by }2 \\ x&=14\end{aligned}\)
Exercise \(\PageIndex{3}\): Solution Pathways
For each equation, try to solve the equation using each method (dividing each side first, or applying the distributive property first). Some equations are easier to solve by one method than the other. When that is the case, stop doing the harder method and write down the reason you stopped.
- \(2,000(x-0.03)=6,000\)
- \(2(x+1.25)=3.5\)
- \(\frac{1}{4}(4+x)=\frac{4}{3}\)
- \(-10(x-1.7)=-3\)
- \(5.4 = 0.3(x+8)\)
Summary
Equations can be solved in many ways. In this lesson, we focused on equations with a specific structure, and two specific ways to solve them.
Suppose we are trying to solve the equation \(\frac{4}{5}(x+27)=16\). Two useful approaches are:
- divide each side by \(\frac{4}{5}\)
- apply the distributive property
In order to decide which approach is better, we can look at the numbers and think about which would be easier to compute. We notice that \(\frac{4}{5}\cdot 27\) will be hard, because 27 isn't divisible by 5. But \(16\div\frac{4}{5}\) gives us \(16\cdot\frac{5}{4}\), and 16 is divisible by 4. Dividing each side by \(\frac{4}{5}\) gives:
\(\begin{aligned} \frac{4}{5}(x+27)&=16 \\ \frac{5}{4}\cdot\frac{4}{5}(x+27)&=16\cdot\frac{5}{4} \\ x+27&=20 \\ x&=-7\end{aligned}\)
Sometimes the calculations are simpler if we first use the distributive property. Let's look at the equation \(100(x+0.06)=21\). If we first divide each side by 100, we get \(\frac{21}{100}\) or 0.21 on the right side of the equation. But if we use the distributive property first, we get an equation that only contains whole numbers.
\(\begin{aligned} 100(x+0.06)&=21 \\ 100x+6&=21 \\ 100x&=15 \\ x&=\frac{15}{100}\end{aligned}\)
Practice
Exercise \(\PageIndex{4}\)
Andre wants to buy a backpack. The normal price of the backpack is $40. He notices that a store that sells the backpack is having a 30% off sale. What is the sale price of the backpack?
(From Unit 4.3.2)
Exercise \(\PageIndex{5}\)
On the first math exam, 16 students received an A grade. On the second math exam, 12 students received an A grade. What percentage decrease is that?
(From Unit 4.3.3)
Exercise \(\PageIndex{6}\)
Solve each equation.
- \(2(x-3)=14\)
- \(-5(x-1)=40\)
- \(12(x+10)=24\)
- \(\frac{1}{6}(x+6)=11\)
- \(\frac{5}{7}(x-9)=25\)
Exercise \(\PageIndex{7}\)
Select all expressions that represent a correct solution to the equation \(6(x+4)=20\).
- \((20-4)\div 6\)
- \(\frac{1}{6}(20-4)\)
- \(20-6-4\)
- \(20\div 6-4\)
- \(\frac{1}{6}(20-24)\)
- \((20-24)\div 6\)
Exercise \(\PageIndex{8}\)
Lin and Noah are solving the equation \(7(x+2)=91\).
Lin starts by using the distributive property. Noah starts by dividing each side by 7.
- Show what Lin's and Noah's full solution methods might look like.
- What is the same and what is different about their methods?