The question is asking for the set of values of $x$ that satisfy the equation $[x] = -2$. The symbol $[x]$ represents the greatest integer less than or equal to $x$ (also known as the floor function).

To solve this:

• The condition $[x] = -2$ means that $x$ must lie between -2 (inclusive) and -1 (exclusive). This is because for any value of $x$ in this range, the greatest integer less than or equal to $x$ is -2.

Thus, the correct interval for $x$ is $-2 \leq x < -1$, which corresponds to option B.

Would you like further details or have any questions?

Here are 5 related questions to expand on the topic:

1. What is the floor function and how is it different from the ceiling function?
2. How does the floor function apply to real numbers, especially negative ones?
3. Can you solve a similar equation with $[x] = 3$? What would be the solution set for $x$?
4. How is the floor function useful in real-life applications?
5. What is the result of $[2.5]$ and $[-2.5]$?

Tip: Always visualize the number line when working with the floor function to understand the intervals where the integer values change.