Solving Single-Step Inequalities by Addition or Subtraction

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How to solve inequalities?
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)

How to solve single-step inequalities by addition or subtraction? How to solve one step linear inequalities in one variable with the variable on the left side?
The solution is graphed and expressed using interval notation.

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