https://file.aiquickdraw.com/mathbot/file/172611298703117omu71v.jpg

The compound inequality shown in the image is:

\[
-601 \leq x \leq -596
\]

This inequality indicates that the variable \( x \) is greater than or equal to -601 and less than or equal to -596. To graph this on a number line:

1. Mark the points -601 and -596 on the number line.
2. Use closed circles at both -601 and -596 since the inequality includes "equal to" (i.e., \( \leq \)).
3. Draw a solid line between -601 and -596 to show that all values between these two points, including the endpoints, satisfy the inequality.

### Explanation of the graph:
- **Closed circles**: These are used because the inequality involves "less than or equal to" (≤) at both endpoints.
- **Solid line**: It connects the two endpoints, indicating that all the values between -601 and -596, inclusive, are part of the solution.

Do you want more details or have any questions?

Here are some related questions to explore further:
1. How would the graph change if the inequality were \( -601 < x \leq -596 \)?
2. What is the difference between a compound inequality with "and" vs. "or"?
3. How would you express this inequality in interval notation?
4. What steps would you follow to solve a system of compound inequalities?
5. How do you graph a compound inequality with both open and closed endpoints?

**Tip**: When graphing inequalities, always pay attention to whether the endpoints are included or not to determine whether to use closed or open circles.

Graph the compound inequality: -601 ≤ x ≤ -596.

Learn how to graph the compound inequality -601 ≤ x ≤ -596 on a number line. This problem focuses on understanding inequalities, using closed circles, and plotting endpoints correctly. Suitable for middle school students in Grades 6-8.

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