<s>[INST] solving given linear equation So before you guys judge me, I honestly am so clueless with this so please bare with my dumb questions.
I have been at this equation that I've been going for an hour now, 
$\frac{(3x-1)}{2} -2 = 5-\frac{4x}{3+1}$ and I'm trying to solve for $x$.
So I go with
$6\cdot(3x-1)/2-2=(5-4x)/3 +1$ to cancel out the denominators, and I get 
$9x+3-6=10-8x+2$
then I move all the like terms, 
$9x+8x=12+9$
then my final answer is
$x=21/17$
that didn't seem correct with me so then I tried, 
cancelling out the denominators by multiplying each side on their own number, 3 and 2. 
then I got $3x-1-2=5-4x+1$
and my answer is 
$x=9/7$
How do I go about solving this?.
 [/INST] Your Equation looks like:
$$\frac {3x+1} {2} - 2 = 5-\frac{4x}{3+1}$$
Adding in the denominator on the right.
$$\frac {3x+1} {2} - 2 = 5-\frac{4x}{4}$$
Which simplifies to
$$\frac {3x+1} {2} - 2 = 5-x$$
We want to eliminate the denominator so we multiply by $2$.
$$ 2\frac {3x+1} {2} - (2)2 = (2)5-(2)x$$
Simplifying
$$3x+1 - 4 = 10-2x$$
Adding on the right.
$$ 3x- 3 = 10-2x$$
Add $2x$ to both sides and add $3$ to both sides.
$$ 5x = 13$$
$$x=\frac{13}{5}$$
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