https://file.aiquickdraw.com/mathbot/file/1730085542281x9am9hcb.jpg

To write the absolute value inequality for the graph on this number line, we need to examine the range of values shown. Here’s the breakdown:

1. The black dots at \(-4\) and \(4\) represent endpoints, indicating the interval between them.
2. The shading extends in both directions from \(-10\) to \(10\), which suggests that the values are between \(-10\) and \(10\).
3. Since the shading includes the range between these two points, this suggests an absolute value inequality.

### Constructing the Inequality

The graph shows values that are less than or equal to \(10\) in distance from \(0\), which we can express with absolute value notation:
\[
|x| \leq 10
\]

This inequality states that \(x\) can range from \(-10\) to \(10\), including both endpoints.

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Would you like more details or have any questions on this?

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Here are 5 related questions for further exploration:

1. How would the inequality change if the shading went only up to \(9\) instead of \(10\)?
2. What would the graph look like if the inequality were \( |x| < 10 \)?
3. How would you write an absolute value inequality for the range \([-5, 5]\)?
4. Can you explain the concept of absolute value in terms of distance on a number line?
5. What is the difference between \( |x| \leq a \) and \( |x| < a \) on a number line?

**Tip:** Absolute value inequalities like \( |x| \leq a \) represent all points within a distance \(a\) from \(0\), which translates visually to an interval on the number line.

Write the absolute value inequality for the given number line graph.

Learn how to write an absolute value inequality based on a number line graph showing the interval from -10 to 10. This problem covers key concepts in algebra, including absolute value and inequalities, suitable for students in Grades 7-9.

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