Answer
$x=\left\{ \dfrac{4}{3},2 \right\}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
|3x-5|+4=5
$ evaluates to
\begin{array}{l}
|3x-5|=1\\
3x-5=1\\
3x=6\\
x=2
,\\\\\text{OR}\\\\
3x-5=-1\\
3x=4\\\\
x=\dfrac{4}{3}
.\end{array}
Hence, the solution set is $
x=\left\{ \dfrac{4}{3},2 \right\}
$.
