https://file.aiquickdraw.com/mathbot/file/1727411910912141btnor.jpg

From the graph you provided, we see two open circles at \( x = -2 \) and \( x = 2 \), which indicate that these values are not included in the solution. The values in between, however, are included. This suggests that the variable \( x \) can take any value between -2 and 2, exclusive.

The absolute value inequality that represents this graph is:
\[ |x| < 2 \]

This inequality states that the absolute value of \( x \) must be less than 2, which corresponds to the range of values for \( x \) from -2 to 2, not including the endpoints themselves.

Would you like any further details on this or have any questions about absolute value inequalities?

Here are some related questions you might find helpful:
1. How would the inequality change if the circles on the graph were closed?
2. What would be the inequality if \( x \) values were greater than 2 and less than -2?
3. How do we solve absolute value inequalities algebraically?
4. Can you explain why absolute values are used in inequalities?
5. How would this inequality be graphed on a coordinate plane?

**Tip:** When writing absolute value inequalities from a number line graph, always check whether the circles are open or closed to determine if the endpoints are included in the inequality.

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

Understand how to write an absolute value inequality based on a graph with open circles at x = -2 and x = 2. This inequality illustrates the range of values that x can take, excluding the endpoints. Suitable for middle school students learning about inequalities.

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