https://file.aiquickdraw.com/mathbot/file/1726904143953zo72eweq.jpg

The image shows a number line graph with two filled circles, located at \(x = -3\) and \(x = 1\). Both of these filled circles suggest that the values include the endpoints at \(x = -3\) and \(x = 1\). The shaded region between these two points indicates that the variable \(x\) lies between these two values.

To write the compound inequality for this graph, we observe:

- The inequality includes the values between \(x = -3\) and \(x = 1\), including both endpoints.
  
Therefore, the compound inequality is:

\[
-3 \leq x \leq 1
\]

This inequality represents all the values of \(x\) between \(-3\) and \(1\), including \(-3\) and \(1\) themselves.

Do you want more details or have any questions? Here are some related questions:

1. What is the difference between "less than" and "less than or equal to" in inequalities?
2. How can we graph a compound inequality like this one?
3. How do open and closed circles on a number line affect the inequality notation?
4. Can inequalities also be written using set notation?
5. How does this inequality relate to interval notation?

**Tip:** When interpreting graphs for inequalities, always check whether the circles are filled or open. This determines if the endpoints are included or excluded.

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

Learn how to write a compound inequality from a number line with endpoints at -3 and 1. This problem involves understanding inequalities and closed intervals. Suitable for students in Grades 6-8.

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