Question

select the correct answer.
which of the following graphs shows the solution set for the inequality below?
$|2x - 2| \leq 4$
a.
b.
c.
d.

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 all parts by 2

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

Step4: Match to number line

Closed dots at $x=-1$ and $x=3$, shaded between them, which matches option C.

Answer:

C. <graph with closed dots at -1 and 3, red line between them on the number line with ticks from -6 to 6>