Math Problem Statement

Which of the following numbers makes the inequality -2 ≤ x < 5 true?

Solution

The inequality in the question is:

2x<5-2 \leq x < 5

We need to determine which number from the choices satisfies this inequality.

Step-by-step analysis:

  • The inequality means that xx must be greater than or equal to -2 but less than 5.
  • Let's analyze each option:

A: -5

  • Is 52-5 \geq -2? No, because 5-5 is less than 2-2. So, this is not a solution.

B: -2

  • Is 22-2 \geq -2? Yes, because 2-2 is equal to 2-2, satisfying the left part.
  • Is 2<5-2 < 5? Yes, because 2-2 is less than 55. Therefore, this is a solution.

C: 5

  • Is 5<55 < 5? No, because 55 is not less than 55, so this is not a solution.

D: 7

  • Is 7<57 < 5? No, because 77 is greater than 55. So, this is not a solution.

E: -3

  • Is 32-3 \geq -2? No, because 3-3 is less than 2-2, so this is not a solution.

Conclusion:

The correct answer is B: -2.

Would you like further details on this?

Here are some related questions to expand on this topic:

  1. What does the inequality ax<ba \leq x < b represent geometrically?
  2. How do you solve compound inequalities involving both << and \leq?
  3. Can you graph the inequality 2x<5-2 \leq x < 5 on a number line?
  4. How do strict and non-strict inequalities affect the solution set?
  5. What are the common mistakes when solving compound inequalities?

Tip: Always double-check whether the inequality includes equality (\leq or \geq) to ensure all boundary values are considered correctly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Inequalities
Algebra

Formulas

x must satisfy both conditions: -2 ≤ x and x < 5

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 6-8