write an absolute - value inequality for the graph below. use x for your variable.

Explanation:

Step1: Find the mid - point

The two points on the number line are $x=-2$ and $x = 2$. The mid - point $c$ of these two points is $\frac{-2 + 2}{2}=0$.

Step2: Find the distance from the mid - point

The distance $d$ from the mid - point $x = 0$ to either of the points $x=-2$ or $x = 2$ is $|2-0|=2$.

Step3: Write the absolute - value inequality

The general form of an absolute - value inequality for the region outside two points symmetric about a mid - point is $|x - c|>d$. Here, $c = 0$ and $d = 2$, so the inequality is $|x|>2$.

Answer:

$|x|>2$