Me with this geometry question image attached

The two answers are the one selected and the choice |x-5| ≤ 1. The steps to solve the other equation are:
|x-5| ≤ 1
x-5 ≤ 1, x-5 ≥ 0
-(x-5) ≤ 6, x-5 is less than 0
x ≤ 6, x ≥ 5
x ≥ 4, x is less than 5
x ∈ [5,6]
x ∈ [4,5]
4 ≤ x ≤ 6
(^which was the original answer^)