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Inequalities

Problems

Properties of Inequalities

Solving Inequalities Using Inverse Operations

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
  2. Addition Property of Inequality
  3. Addition
  4. Additive Identity Property
  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. 1x≥ -
  6. x≥ -

  1. Given
  2. Subtraction Property of Inequality
  3. Subtraction
  4. Additive Identity Property
  5. Division Property of Inequality (for negative numbers)
  6. Division
  7. Multiplicative Identity Property

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