Answer
$(-\infty,-8) \cup (16, \infty)$
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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$|3-\displaystyle \frac{3}{4}x| \gt 9\Rightarrow \left\{\begin{array}{ll}
3-\frac{3}{4}x\lt -9 & \\
or & \\
3-\frac{3}{4}x \gt 9 &
\end{array}\right.$
$ \begin{array}{lllll}
3-\frac{3}{4}x\lt -9 & /\times 4 & ...or... & 3-\frac{3}{4}x \gt 9 & /\times 4\\
12-3x\lt -36 & /-12 & & 12-3x \gt 36 & /-12\\
-3x\lt -48 & /\div(-3) & & -3x \gt 24 & /\div(-3)\\
& (neg!) & & & (neg!)\\
x\gt 16 & & & x \lt -8 & \\
x\in(16,\infty) & & or & x\in(-\infty,-8) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-8) \cup (16, \infty)$
