Math Problem Statement

Which of the following inequalities are correct?

Some of the numbers involved are shown on the number line below.

Choose all answers that apply:

Choose all answers that apply:

(Choice A)   

[-7,,\ <, -5]

A

[-7,,\ <, -5]

(Choice B)   

[-7,,\ <,,,,,,\ 0]

B

[-7,,\ <,,,,,,\ 0]

(Choice C)   

[,,,,,7,,\ >, -7]

C

[,,,,,7,,\ >, -7]

Solution

Let's evaluate each inequality:

Choice A:
7<5-7 < -5 This is correct because on the number line, 7-7 is to the left of 5-5, meaning 7-7 is less than 5-5.

Choice B:
7<0-7 < 0 This is correct because 7-7 is to the left of 00 on the number line, so 7-7 is less than 00.

Choice C:
7>77 > -7 This is also correct because 77 is to the right of 7-7 on the number line, meaning 77 is greater than 7-7.

Correct answers:

  • Choice A: 7<5-7 < -5
  • Choice B: 7<0-7 < 0
  • Choice C: 7>77 > -7

Do you want more details or have any questions?

Here are 5 related questions:

  1. What is the significance of the number line when comparing numbers?
  2. Can a negative number ever be greater than a positive number?
  3. What is the relationship between absolute values and inequalities?
  4. How does multiplying or dividing both sides of an inequality by a negative number affect the inequality?
  5. How do inequalities change when shifting all terms by a constant value?

Tip: When comparing numbers on a number line, remember that numbers to the right are always greater than those to the left.

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Math Problem Analysis

Mathematical Concepts

Number Line
Inequalities
Comparing Negative and Positive Numbers

Formulas

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Theorems

Properties of Inequalities
Number Line Ordering

Suitable Grade Level

Grades 6-8