https://file.aiquickdraw.com/mathbot/file/1726112000518msvphe6o.jpg

The compound inequality given in the image is:

\[
-9 < x \leq -8
\]

### Steps to graph this inequality:

1. **Plot the endpoint at \(-9\):**
   Since the inequality is strict at \(-9\) (i.e., \( -9 < x \)), the point at \(-9\) should be **open** on the number line. This indicates that \(-9\) is **not** included in the solution set.

2. **Plot the endpoint at \(-8\):**
   Since the inequality is \( x \leq -8 \), the point at \(-8\) should be **closed**. This indicates that \(-8\) is **included** in the solution set.

3. **Shade the interval:**
   The interval to shade is between \(-9\) (open) and \(-8\) (closed). So, the region between these two points on the number line should be highlighted or connected with a segment.

In summary:
- **Open circle** at \(-9\)
- **Closed circle** at \(-8\)
- Line connecting these points to indicate the solution.

Do you want more details, or do you have any questions?

### Related questions:
1. What is the difference between open and closed intervals?
2. How do you solve compound inequalities with more than two inequalities?
3. Can you graph inequalities involving greater than or less than without endpoints?
4. How can you write the solution of a compound inequality in interval notation?
5. How do compound inequalities change if both sides are multiplied by a negative number?

#### Tip:
Always pay attention to whether the inequality is strict ( \(<\) or \(>\) ) or inclusive ( \(\leq\) or \(\geq\) ) to correctly plot the endpoints.

Graph the compound inequality: -9 < x ≤ -8

Learn how to graph the compound inequality -9 < x ≤ -8 on a number line. This problem focuses on the concepts of strict and inclusive inequalities, appropriate for students in Grades 6-8.

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