#### Answer

$\displaystyle x=\frac{25}{6}$
$\displaystyle x=-\frac{65}{6}$

#### Work Step by Step

$|\displaystyle \frac{3}{5}x+2|-\frac{1}{2}=4$
$|\frac{3}{5}x+2|=4+\frac{1}{2}=\frac{9}{2}$
We split the absolute value into two equations, the positive and negative:
$\displaystyle \frac{3}{5}x+2=\frac{9}{2}$
$\displaystyle \frac{3}{5}x=\frac{5}{2}$
$\displaystyle x=\frac{25}{6}$
$\displaystyle \frac{3}{5}x+2=-\frac{9}{2}$
$\displaystyle \frac{3}{5}x=-\frac{13}{2}$
$\displaystyle x=-\frac{65}{6}$