Solving One-Step Linear Inequalities

Inequalities are mathematical sentences comparing two quantities that are not equal (or possibly not equal). There are five inequality symbols:

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.

$\begin{array}{l} n + 8 - 8 < 10 - 8 \\ n < 2 \end{array}$

Example 2:

Solve for $y$ .

$- 3 y \geq 15$

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.

$\begin{array}{l} \frac{- 3 y}{- 3} \leq \frac{15}{- 3} \\ y \leq - 5 \end{array}$

When you're done solving an inequality, you may be asked to graph it. See the lesson on Graphing Linear Inequalities if you need help.