https://file.aiquickdraw.com/mathbot/file/1726929702195s1gycm16.jpg

The graph provided shows two open circles at \( x = -2 \) and \( x = 4 \), with shading between these points. Since the circles are open, it indicates that the values at \( -2 \) and \( 4 \) are not included in the solution.

To write a compound inequality for this graph:

\[
-2 < x < 4
\]

This inequality means that \( x \) lies between \( -2 \) and \( 4 \), but does not include \( -2 \) or \( 4 \) themselves.

Would you like further explanation or have any questions?

Here are five related questions to expand on this:

1. How would the inequality change if the circles were closed?
2. How do you graph an inequality with one side open and the other side closed?
3. What is the difference between strict and non-strict inequalities in terms of graphing?
4. How would the graph look if the inequality were \( -2 \leq x \leq 4 \)?
5. How can you solve compound inequalities algebraically?

**Tip:** Always look at whether the circles are open or closed on the number line to determine whether to use strict (\(<\)) or non-strict (\(\leq\)) inequalities.

Write a compound inequality for the graph shown below. Use x for your variable.

Understand how to write the compound inequality -2 < x < 4 based on a graph with open circles. This problem covers key algebraic concepts like inequalities and the visual representation of open intervals. Suitable for students in Grades 7-9.

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