https://file.aiquickdraw.com/mathbot/file/17291191525271ta05cmw.jpg

The image shows a number line with two points marked at \(-6\) and \(-2\), connected by a line between them. This indicates a range of values for the variable \(x\), suggesting that the compound inequality involves the interval between \(-6\) and \(-2\).

Because the points at \(-6\) and \(-2\) are filled in (solid dots), it means that the endpoints are included, so the inequality should use "less than or equal to" symbols.

The compound inequality would be:

\[
-6 \leq x \leq -2
\]

This means that \(x\) is greater than or equal to \(-6\) and less than or equal to \(-2\).

Would you like further details or have any questions?

Here are five related questions to explore further:
1. What is the difference between strict inequalities and inclusive inequalities?
2. How would the inequality change if one of the endpoints had an open circle?
3. How can compound inequalities be solved when variables appear on both sides?
4. Can you graph a similar inequality for values between 3 and 7?
5. How do you represent a union of inequalities on a number line?

**Tip**: When solving compound inequalities, remember that "and" means both conditions must be true, while "or" means at least one condition is true.

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

Learn how to write a compound inequality for a number line graph between -6 and -2. This problem involves understanding compound inequalities and interpreting number lines, perfect for students in Grades 6-8.

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