Answer
$$x=-\frac{8}{3}\quad \mathrm{or}\quad \:x=\frac{8}{3}$$
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:
$$ 2+\left|3x\right|=10\\ \left|3x\right|=8\\ 3x=-8\quad \mathrm{or}\quad \:3x=8\\ x=-\frac{8}{3}\quad \mathrm{or}\quad \:x=\frac{8}{3}$$
