Answer
$x=\left\{ -30,30 \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|0.3x|=9
,$ is equivalent to
\begin{array}{l}\require{cancel}
0.3x=9 \text{ OR } 0.3x=-9
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
0.3x=9
\\\\
10(0.3x)=(9)10
\\\\
3x=90
\\\\
x=\dfrac{90}{3}
\\\\
x=30
\\\\\text{ OR }\\\\
0.3x=-9
\\\\
10(0.3x)=(-9)10
\\\\
3x=-90
\\\\
x=-\dfrac{90}{3}
\\\\
x=-30
.\end{array}
Hence, the solutions are $
x=\left\{ -30,30 \right\}
.$