Use the definition of absolute value,
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
If x - 1 ≥ 0, then |x - 1| = x - 1, and so
|x - 1| = 5x + 2
x - 1 = 5x + 2
4x = -3
x = -3/4
Otherwise, if x - 1 < 0, then |x - 1| = -(x - 1), which means
|x - 1| = 5x + 2
-x + 1 = 5x + 2
6x = -1
x = -1/6
