Answer
$x=\left\{ \dfrac{1}{5},1 \right\}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
|5x-3|+2=4
$ evaluates to
\begin{array}{l}
|5x-3|=2\\
5x-3=2\\
5x=5\\
x=1
,\\\\\text{OR}\\\\
5x-3=-2\\
5x=1\\\\
x=\dfrac{1}{5}
.\end{array}
Hence, the solution set is $
x=\left\{ \dfrac{1}{5},1 \right\}
$.
