Solving One-Step Linear Inequalities

Some linear inequalities can be solved with a single operation. For this type of inequality, use the inverse operation to solve.

Example 1:

Solve for n.

n + 8 < 10

The inverse operation of addition is subtraction. So, subtract 8 from both sides.

n + 8 – 8 < 10 – 8

n < 2

Example 2:

Solve for y.

–3y ≥ 15

The inverse operation of multiplication is division. So, divide both sides by –3.

IMPORTANT: Whenever you multiply or divide both sides of an inequality by a negative number, reverse the inequality.

(–3y)/(–3) ≤ 15/(–3)

y ≤ 5