Answer
$x=\dfrac43$, $x=-\dfrac27$
Work Step by Step
$|5x-1|=|2x+3|$
$5x-1=2x+3~~~~~~~~~~~\text{or}~~~~~~~~~~~~~5x-1=-(2x+3)$
$5x-2x=1+3~~~~~~~~~~~\text{or}~~~~~~~~~~~~~5x-1=-2x-3$
$3x=4~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{or}~~~~~~~~~~~~~7x=-2$
$x=\dfrac43~~~~~~~~~~~~~~~~~~~~~~~~~~~\text{or}~~~~~~~~~~~~~x=-\dfrac27$
