Solving Single-Step Inequalities by Addition or Subtraction

The rules for solving inequalities are similar to those for solving linear equations. However, there is one exception, when multiplying or dividing by a negative number it is necessary to reverse the inequality sign.

Solving Single-Step Inequalities by Addition

Example :

Solve x – 6 > 14

Solution:

x – 6 > 14

x – 6+ 6 > 14 + 6

x > 20

Example :

Solve the inequality –7 – x < 9

Solution:

–7 – x < 9

7 – x + 7 < 9 + 7

– x < 16

x > –16 (multiply both sides by –1 and reverse the sign)

Solving Single-Step Inequalities by Subtraction

Example:

Solve x + 7 < 15

Solution:

x + 7 < 15

x + 7 – 7 < 15 – 7

x < 8

Example :

Solve the inequality 12 > 18 – y

Solution:

12 > 18 – y

18 – y < 12

18 – y – 18 < 12 –18

– y < –6

y > 6 (multiply both sides by –1 and reverse the sign)

The following video shows how to solve single-step inequalities by addition or subtraction.

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