Answer
$x=\dfrac{24}{5} ~or~x=-\dfrac{36}{5} $.
Work Step by Step
Using the definition of the absolute value, we have
$$\displaystyle
|\frac{x}{3}+\frac{2}{5}|=2\Longrightarrow \frac{x}{3}+\frac{2}{5}=2~ or~ \frac{x}{3}+\frac{2}{5}=-2\\
\Longrightarrow \frac{x}{3}=2-\frac{2}{5}=\frac{8}{5}~ or~ \frac{x}{3}=-2-\frac{2}{5}=-\frac{12}{5}\\
.$$
Thus, we solve the two possible equations:
$\dfrac{x}{3}=\dfrac{8}{5}$
$x=\dfrac{8*3}{5}=\dfrac{24}{5}$
or
$\dfrac{x}{3}=-\dfrac{12}{5}$
$x=-\dfrac{12*3}{5}=-\dfrac{36}{5}$
