The given image shows a number line with a range marked between $-12$ and $-6$, both included. We can represent this range as an absolute value inequality.

To find the absolute value inequality, follow these steps:

1. The middle point between $-12$ and $-6$ is the average: $\frac{-12 + (-6)}{2} = \frac{-18}{2} = -9$ So, the center of the interval is $-9$.

2. Next, calculate the distance from $-9$ to either endpoint (since the interval is symmetric): $| -9 - (-12) | = 3 \quad \text{or} \quad | -9 - (-6) | = 3$ So, the distance from the center is 3.

Thus, the absolute value inequality can be written as: $| x + 9 | \leq 3$

This inequality represents all the values of $x$ that lie within 3 units of $-9$, which is equivalent to the interval $[-12, -6]$.

Would you like further details on how to interpret this inequality or more examples? Here are five related questions to consider:

1. How do you solve an absolute value inequality like $|x - a| \leq b$?
2. What are the steps to graph an absolute value inequality?
3. How do you interpret an absolute value inequality involving "greater than" (e.g., $|x - a| \geq b$)?
4. How would this inequality change if the interval were $(-12, -6]$ instead of $[-12, -6]$?
5. How can you solve compound inequalities graphically?

Tip: When working with absolute value inequalities, always visualize the problem on a number line to better understand the range of solutions.