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# Inequalities

Math
• Study Guide
Summary

## Problems 2

Summary Problems 2

Problem : What property is demonstrated by the following statement?
5 > 2 and 2 > 0. Thus 5 > 0.

Transitive Property of Inequality

Problem : If x is a positive real number, which inequality sign goes in the circle? What property does this show?
- x 0

<, by the Inequality Property of Opposites

Problem : If x and y are positive real numbers, which inequality sign goes in the circle?
x < y   >

Problem : Name the property or operation used in each of the following steps:

1. 2x < 5 - x
2. 2x + x < 5 - x + x
3. 3x < 5 + 0
4. 3x < 5
5. < 6. 1x < 7. x < 1. Given
5. Division Property of Inequality (for positive numbers)
6. Division
7. Multiplicative Identity Property

Problem : Name the property or operation used in each of the following steps:

1. -2xx + 5
2. -2x - xx + 5 - x
3. -3x≤0 + 5
4. -3x≤5
5.  6. 1x≥ - 7. x≥ - 1. Given
2. Subtraction Property of Inequality
3. Subtraction