Answer
$(-\infty,-5]\cup[3,\infty)$
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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$|\displaystyle \frac{2x+2}{4}| \geq 2\Rightarrow \left\{\begin{array}{ll}
\frac{2x+2}{4}\leq -2 & \\
or & \\
\frac{2x+2}{4} \geq 2 &
\end{array}\right.$
$ \begin{array}{lllll}
\frac{2x+2}{4} \leq -2 & /\times 4 & ...or... & \frac{2x+2}{4}\geq 2 & /\times 4\\
2x+2\leq-8 & /-2 & & 2x+2\geq 8 & /-2\\
2x\leq-10 & /\div 2 & & 2x\geq 6 & /\div 2\\
x\leq-5 & & & x\geq 3 & \\
x\in(-\infty,-5] & & or & x\in[3,\infty) & \\
& & & &
\end{array} $
Solution set: $(-\infty,-5]\cup[3,\infty)$
