Answer
$(-\infty,-2]\cup[4,\infty)$
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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$|\displaystyle \frac{3x-3}{9}| \geq 1\Rightarrow \left\{\begin{array}{ll}
\frac{3x-3}{9}\leq -1 & \\
or & \\
\frac{3x-3}{9} \geq 1 &
\end{array}\right.$
$ \begin{array}{lllll}
\frac{3x-3}{9} \leq -1 & /\times 9 & ...or... & \frac{3x-3}{9}\geq 1 & /\times 9\\
3x-3\leq-9 & /+3 & & 3x-3\geq 9 & /+3\\
3x\leq-6 & /\div 3 & & 3x\geq 12 & /\div 3\\
x\leq-2 & & & x\geq 4 & \\
x\in(-\infty,-2] & & or & x\in[4,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-2]\cup[4,\infty)$
