https://file.aiquickdraw.com/mathbot/file/172675674594898gjyyf5.png

The graph shows two open circles at \(x = -3\) and \(x = 4\), with a line connecting the two points. This suggests that the inequality includes all values between \(x = -3\) and \(x = 4\), but does not include \(x = -3\) or \(x = 4\) themselves.

To express this as an absolute value inequality, first observe that the midpoint between \(-3\) and 4 is \(\frac{-3 + 4}{2} = 0.5\). The distance from the midpoint \(0.5\) to either endpoint is \(\frac{4 - (-3)}{2} = 3.5\).

The absolute value inequality will therefore express that the distance from \(x\) to the midpoint \(0.5\) is less than \(3.5\). The inequality can be written as:

\[
|x - 0.5| < 3.5
\]

This inequality describes all the values of \(x\) that lie between \(-3\) and 4, excluding the endpoints.

Would you like more details or explanations?

Here are 5 related questions to consider:
1. How do you convert other types of intervals into absolute value inequalities?
2. What would the inequality look like if the circles were closed?
3. How do you solve absolute value inequalities step by step?
4. Can you graph the solution of a more complex absolute value inequality?
5. How would the inequality change if the points were at different locations?

**Tip**: To graph absolute value inequalities, always start by identifying the midpoint and the distance to the endpoints.

Write an absolute value inequality for the graph below. The graph shows open circles at x = -3 and x = 4.

Learn how to write an absolute value inequality for a graph with open circles at x = -3 and x = 4. This problem involves identifying the midpoint and the distance to the endpoints. Suitable for students in Grades 8-10.

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