https://file.aiquickdraw.com/mathbot/file/17264514568334q64idjj.jpg

The compound inequality in the image is:

\[
x \leq -1 \quad \text{or} \quad x \geq 2
\]

This inequality can be solved as follows:

- **First part**: \( x \leq -1 \)
- **Second part**: \( x \geq 2 \)

This is an "or" inequality, meaning that \( x \) can satisfy either one or both conditions. Therefore, the solution is the union of these two intervals.

### Solution set:
- The solution consists of all values of \( x \) that are less than or equal to \(-1\), and all values of \( x \) that are greater than or equal to \(2\).
  
This can be written in interval notation as:

\[
(-\infty, -1] \cup [2, \infty)
\]

### Now, let's analyze the answer choices based on this understanding:

- **Choice A** is incorrect because the inequality symbols or the number ranges seem to be wrong.
- **Choice B** correctly matches the inequality. It will likely say:
  
  \[
  \{ x \mid x \leq -1 \quad \text{or} \quad x \geq 2 \}
  \]

- **Choice C** ("The solution is all real numbers") is incorrect because the solution set does not cover all real numbers.
- **Choice D** ("There is no solution") is also incorrect, since there are solutions for \( x \leq -1 \) or \( x \geq 2 \).

### Final Answer:
**Choice B** is the correct answer.

Let me know if you'd like further details or explanations!

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Here are 5 related questions to deepen your understanding:
1. How do you solve compound inequalities with "and" versus "or" conditions?
2. Can a compound inequality ever have no solution?
3. What is the difference between an inequality with "or" and one with "and"?
4. How can you graph the solution of a compound inequality on a number line?
5. How would you solve a compound inequality that involves absolute values?

**Tip**: When dealing with "or" inequalities, think of the union of two separate solution sets—any solution that satisfies one or both parts works!

Solve the compound inequality: x ≤ -1 or x ≥ 2. Select the correct choice and graph the solution on a number line.

Learn how to solve the compound inequality x ≤ -1 or x ≥ 2. This question tests key algebra concepts, focusing on graphing the solution on a number line and understanding compound inequalities with 'or' conditions. Suitable for students in Grades 7-9.

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