Answer
$$x=-42\quad \mathrm{or}\quad \:x=38$$
Work Step by Step
Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find:
$$ \frac{x+2}{5}=-8\quad \mathrm{or}\quad \frac{x+2}{5}=8\\ x=-42\quad \mathrm{or}\quad \:x=38$$
