Answer
$x=6 \hspace{20pt}\text{ OR }\hspace{20pt}x=-6$
Work Step by Step
Since for any $c\gt0$, $|x|=c$ implies $x=c \hspace{8pt}\text{ or } \hspace{8pt}x=-c,$ the given equation, $
|3x|=18
,$ is equivalent to
\begin{array}{l}\require{cancel}
3x=18
\\\\\text{OR}\\\\
3x=-18
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x=18
\\
\dfrac{3x}{3}=\dfrac{18}{3}
\\
x=6
\\\\\text{OR}\\\\
3x=-18
\\
\dfrac{3x}{3}=-\dfrac{18}{3}
\\
x=-6
.\end{array}
Hence,
$
x=6\hspace{20pt}\text{ OR }\hspace{20pt}x=-6
$
