https://file.aiquickdraw.com/mathbot/file/1726386637032w16iiwhy.jpg

The problem in the image asks for the set of \( x \)-values that satisfy the equation \( [x] = -2 \), where \( [x] \) represents the floor function (the greatest integer less than or equal to \( x \)).

### Understanding the Floor Function:
The floor function \( [x] = -2 \) means that \( x \) is any real number such that its floor is equal to \( -2 \). This will happen when \( -2 \leq x < -1 \). 

This is because:
- If \( x = -2 \), the floor of \( x \) is \( -2 \).
- If \( x = -1.5 \), the floor of \( x \) is still \( -2 \).
- But if \( x = -1 \), the floor of \( x \) becomes \( -1 \), not \( -2 \).

Thus, the interval for \( x \) is \( -2 \leq x < -1 \).

### Correct Answer:
The correct option is **(B) \( -2 \leq x < -1 \)**.

---

Would you like further details or clarifications on this? Here are 5 questions related to this concept:

1. What is the definition of the floor function?
2. How does the floor function behave for negative values of \( x \)?
3. What is the difference between the floor function and the ceiling function?
4. Can the floor function be applied to non-integer values?
5. How do you graph the floor function?

**Tip:** The floor function rounds a number down to the nearest integer, regardless of whether the number is positive or negative.

مجموعة قيم x التي تحقق المعادلة [x] = -2 هي:

This problem asks to find the set of values of x that satisfy the equation [x] = -2. Learn how to work with the floor function and inequalities, applicable for high school students. The correct answer is the interval -2 ≤ x < -1.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation