Math Problem Statement
Which of the following numbers makes the inequality -2 ≤ x < 5 true?
Solution
The inequality in the question is:
We need to determine which number from the choices satisfies this inequality.
Step-by-step analysis:
- The inequality means that must be greater than or equal to -2 but less than 5.
- Let's analyze each option:
A: -5
- Is ? No, because is less than . So, this is not a solution.
B: -2
- Is ? Yes, because is equal to , satisfying the left part.
- Is ? Yes, because is less than . Therefore, this is a solution.
C: 5
- Is ? No, because is not less than , so this is not a solution.
D: 7
- Is ? No, because is greater than . So, this is not a solution.
E: -3
- Is ? No, because is less than , 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:
- What does the inequality represent geometrically?
- How do you solve compound inequalities involving both and ?
- Can you graph the inequality on a number line?
- How do strict and non-strict inequalities affect the solution set?
- What are the common mistakes when solving compound inequalities?
Tip: Always double-check whether the inequality includes equality ( or ) to ensure all boundary values are considered correctly.
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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