What is the sum of all values of x which |x-3|+|3-x|-1=?
If x>=3,
|x-3| = x-3
|3-x| = x-3
So,
2x-6 = 1
2x = 7
x = 7/2
If x < 3,
|x-3| = 3-x
|3-x| = 3-x
So,
6-2x = 1
2x = 5
x = 5/2
In either case, |x-3| and |3-x| are the distance of x from 3. Twice that distance = 1, so x is 1/2 away from 3, in either direction.