First of all we have the condition (because the left side is ). So, .
But, for we have .
So, the inequality stands for all .
You have only to understand this concept:
If x >= 0, then |x| = x -- The absolute value does nothing to a nonnegative value.
If x < 0, then |x| = -x -- Example, |-3| = -(-3) = 3
So, you have
|x-1|
For x-1 >= 0, or x >= 1, |x-1| = x-1. Solve x-1 = 1-x, but ONLY for x >= 1
For x-1 < 0, or x < 1, |x-1| = -(x-1) = 1-x. Solve 1-x = 1-x, but ONLY for x < 1
Let's see what you get.