The problem asks to find the range of values of $x$ that satisfy the equation $\lfloor x \rfloor = -2$, where $\lfloor x \rfloor$ represents the greatest integer less than or equal to $x$.

For $\lfloor x \rfloor = -2$, $x$ must be in the range where the greatest integer less than or equal to $x$ is -2. This occurs when:

$-2 \leq x < -1$

Thus, the correct range for $x$ is $-2 \leq x < -1$.

The correct answer is B.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. What is the mathematical definition of the floor function $\lfloor x \rfloor$?
2. How does the floor function differ from the ceiling function $\lceil x \rceil$?
3. How would you solve $\lfloor x \rfloor = 3$?
4. What is the graph of the floor function $\lfloor x \rfloor$ like?
5. How does the floor function behave for negative values of $x$?

Tip: The floor function rounds down to the nearest integer, even for negative values.