Answer
$x=\{ -6,6 \}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|5x|=30
,$ is equivalent to
\begin{array}{l}\require{cancel}
5x=30 \text{ OR } 5x=-30
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5x=30
\\\\
x=\dfrac{30}{5}
\\\\
x=6
\\\\\text{ OR }\\\\
5x=-30
\\\\
x=-\dfrac{30}{5}
\\\\
x=-6
.\end{array}
Hence, the solutions are $
x=\{ -6,6 \}
.$