## Precalculus (6th Edition) Blitzer

$(-\infty,-5]\cup[3,\infty)$
The solutions of $|u|\gt c$ are the numbers that satisfy $u\lt -c$ or $u\gt c.$ --- $|\displaystyle \frac{2x+2}{4}| \geq 2\Rightarrow \left\{\begin{array}{ll} \frac{2x+2}{4}\leq -2 & \\ or & \\ \frac{2x+2}{4} \geq 2 & \end{array}\right.$ $\begin{array}{lllll} \frac{2x+2}{4} \leq -2 & /\times 4 & ...or... & \frac{2x+2}{4}\geq 2 & /\times 4\\ 2x+2\leq-8 & /-2 & & 2x+2\geq 8 & /-2\\ 2x\leq-10 & /\div 2 & & 2x\geq 6 & /\div 2\\ x\leq-5 & & & x\geq 3 & \\ x\in(-\infty,-5] & & or & x\in[3,\infty) & \\ & & & & \end{array}$ Solution set: $(-\infty,-5]\cup[3,\infty)$