Answer
$(-\infty,-3) \cup (12, \infty)$
Work Step by Step
The solutions of $|u|\gt c $ are the numbers that satisfy $ u\lt -c $ or $ u\gt c.$
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$|3-\displaystyle \frac{2}{3}x| \gt 5\Rightarrow \left\{\begin{array}{ll}
3-\frac{2}{3}x\lt -5 & \\
or & \\
3-\frac{2}{3}x \gt 5 &
\end{array}\right.$
$ \begin{array}{lllll}
3-\frac{2}{3}x\lt -5 & /\times 3 & ...or... & 3-\frac{2}{3}x \gt 5 & /\times 3\\
9-2x\lt -15 & /-9 & & 9-2x \gt 15 & /-9\\
-2x\lt -24 & /\div(-2) & & -2x \gt 6 & /\div(-2)\\
& (negative!) & & & (negative!)\\
x\gt 12 & & & x \lt -3 & \\
x\in(12,\infty) & & or & x\in(-\infty,-3) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-3) \cup (12, \infty)$
