select the correct answer. which of the following graphs shows the solution set for the inequality below…

Explanation:

Step1: Rewrite absolute value inequality

$-4 \leq 2x - 2 \leq 4$

Step2: Add 2 to all parts

$-4 + 2 \leq 2x \leq 4 + 2$ $\implies -2 \leq 2x \leq 6$

Step3: Divide by 2 on all parts

$\frac{-2}{2} \leq x \leq \frac{6}{2}$ $\implies -1 \leq x \leq 3$

Step4: Match to graph

The solution is all $x$ between -1 and 3, inclusive, which corresponds to a number line with closed dots at -1 and 3, and the segment between them shaded.

Answer:

D. <graph with closed dots at -1 and 3, shaded segment between them>