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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.

مجموعة قيم x التي تحقق المعادلة ⌊x⌋ = -2 هي؟

Learn how to solve ⌊x⌋ = -2 and find the corresponding range for x. This problem covers the floor function concept and its application to inequalities. Suitable for students in Grades 8-10.

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