https://file.aiquickdraw.com/mathbot/file/1726756685873z91czin6.png

The number line in the image shows the solution to an absolute value inequality. The endpoints are at \( x = -2 \) and \( x = 2 \), and the region between them is shaded, indicating the values of \( x \) that satisfy the inequality.

To write the absolute value inequality that represents this graph, you can follow these steps:

1. The center of the interval is the midpoint between \(-2\) and \(2\), which is 0.
2. The distance from the center (0) to either endpoint (2 or \(-2\)) is 2.

Thus, the absolute value inequality that describes the graph is:

\[
|x| \leq 2
\]

This inequality means that the distance of \(x\) from 0 is less than or equal to 2, which matches the shaded region between \(-2\) and \(2\) on the graph.

Do you need further details or explanations? Here are five related questions to expand on this concept:

1. How would you write an absolute value inequality for a range between -5 and 5?
2. What would change in the inequality if the points were open circles instead of closed?
3. How can you express the same inequality \( |x| \leq 2 \) without using absolute value?
4. What is the general form of an absolute value inequality for a range between \(a\) and \(b\)?
5. How would the inequality change if the interval was shifted to the right?

**Tip:** The absolute value inequality \( |x - c| \leq r \) describes all values of \(x\) within \(r\) units of \(c\).

Write an absolute value inequality for the graph below. Use x for your variable.

This lesson covers how to write an absolute value inequality based on a number line. The solution explains the inequality |x| ≤ 2, describing the region between -2 and 2. Suitable for students in Grades 7-9.

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