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

Explanation:

Step1: Find the mid - point

The two critical points are $x=-6$ and $x = 6$. The mid - point between them is $\frac{-6 + 6}{2}=0$.

Step2: Find the distance from the mid - point to a critical point

The distance from $0$ to $6$ (or from $0$ to $-6$) is $d = 6$.

Step3: Write the absolute - value inequality

The graph represents all $x$ values such that the distance between $x$ and $0$ is greater than $6$. The absolute - value inequality is $|x|>6$.

Answer:

$|x|>6$