https://file.aiquickdraw.com/mathbot/file/1726756601489a67sdre0.png

The number line in the graph represents values between \(-7\) and \(7\). These points are marked as open circles, which means they are **not included** in the solution set. The goal is to write an **absolute value inequality** that describes this range.

The center point of this range is \(0\), and the distance from \(0\) to either endpoint is 7. Therefore, the inequality will be of the form:

\[
|x| < 7
\]

This inequality states that the distance of \(x\) from 0 is less than 7, covering all values between \(-7\) and \(7\), but not including \(-7\) and \(7\) themselves (open circles).

Thus, the **absolute value inequality** for the given graph is:

\[
|x| < 7
\]

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How would the inequality change if the circles were closed instead of open?
2. Can absolute value inequalities also have solutions outside a range? What would that look like?
3. How do you solve an absolute value inequality like \( |x - 3| > 5 \)?
4. What is the difference between \( |x| < a \) and \( |x| \leq a \) in terms of graphing on a number line?
5. How can you write compound inequalities without absolute values for cases like this?

**Tip**: Always remember that open circles on a number line represent strict inequalities (\(<\) or \(>\)), while closed circles represent inclusive inequalities (\(\leq\) or \(\geq\)).

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

Learn how to write an absolute value inequality for a number line showing values between -7 and 7. This problem covers the concept of absolute value inequalities and demonstrates how to interpret open circles on a graph. Suitable for students in Grades 7-9.

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