Answer
$(-\infty,-5]\cup[3,\infty)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | \frac{2x+2}{4}\right |\geq2$
Rewrite the inequality without absolute value bars.
$\Rightarrow \frac{2x+2}{4}\leq-2$ or $\frac{2x+2}{4}\geq2$
Solve each inequality separately.
Multiply all parts by $4$.
$\Rightarrow \frac{2x+2}{4}(4)\leq-2(4)$ or $\frac{2x+2}{4}(4)\geq2(4)$
Simplify.
$\Rightarrow 2x+2\leq-8$ or $2x+2\geq8$
Add $-2$ to all parts.
$\Rightarrow 2x+2-2\leq-8-2$ or $2x+2-2\geq8-2$
Simplify
$\Rightarrow 2x\leq-10$ or $2x\geq6$
Divide all parts by $2$.
$\Rightarrow \frac{2x}{2}\leq\frac{-10}{2}$ or $\frac{2x}{2}\geq\frac{6}{2}$
Simplify.
$\Rightarrow x\leq-5$ or $x\geq3$
The solution set is less than or equal to $-5$ or greater than or equal to $3$.
The interval notation is
$(-\infty,-5]\cup[3,\infty)$.
