How to Solve Inequalities Using More Than One Property

A greater-than or less-than sign defines the relationship between two sides of an inequality equation. This signifies the two sides are not equal. You use the same algebraic rules to manipulate and solve these equations as you would with equations with equal signs. The basic properties governing inequalities reflect this fact. However, property three is the exception. Property three states: whenever you multiply or divide through by a negative number, the inequality sign changes. A less-than sign changes into a greater-than sign and the greater-than sign changes into a less-than sign.

Instructions

    • 1

      Specify the inequality equation. As an example, use:

      2x + 3 > 7x + 4

    • 2

      Solve the equation to combine like terms. Be sure to follow the order of operation to manipulate equations. The proper order is reflected in the acronym PEMDAS, which stands for parentheses, exponents, multiplication and division, and then addition and subtraction.

    • 3

      Use the example 2x + 3 > 7x +4. Subtract 7x from both sides to get the x terms on the left side of the equation.

      2x + 3 - 7x > 7x + 4 - 7x

      -5x + 3 > 4

    • 4

      Subtract 3 from both sides to get the constant term on the right side.

      -5x + 3 - 3> 4 - 3

      -5x > 1

      Note: This example addresses property #1 where you add and subtract numbers from both sides of the inequality.

    • 5

      Solve the equation to get x on the left side of the equation by itself. Continuing with the example, divide both sides by 5.

      -5x/5 > 1/5

      -x > 1/5

    • 6

      Multiply both sides by -1 to convert -x to x. Multiplying through by a negative number changes the inequality sign.

      -x (-1) > 1/5(-1)

      x < -1/5

      Note 1: This example addresses property #3.

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