I know that the absolute value of a number is its distance from zero on the number line, regardless of the direction. So, to find the values of $x$ that satisfy the equation, I need to think of two numbers that are 7 units away from 1 on the number line. One such number is 1 + 7 = 8, because if I start at 1 and move 7 units to the right, I end up at 8. Another such number is 1 - 7 = -6, because if I start at 1 and move 7 units to the left, I end up at -6. These are the only two values of $x$ that satisfy the equation, because any other number would be either closer or farther than 7 units from 1. To find the sum of these two values, I just add them together: 8 + (-6) = 2. 
Find the sum of all values of $x$ such that $|x-1| = 7$.