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!

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!