Two-Step Inequalities

A two-step inequality is an inequality that requires two operations to isolate the variable. It often involves addition or subtraction followed by multiplication or division.

Add 4 to both sides: -8k ≤ -56. Then divide by -8 (remember to flip the inequality): k ≥ 7.

It means that the value of k must be 7 or greater to satisfy the inequality.

Add 1 to both sides: u/7 ≤ 2. Then multiply by 7: u ≤ 14.

Add 1 to both sides: 7n > 77. Then divide by 7: n > 11.

It indicates that the value of c must be greater than 3.

Subtract 4 from both sides: 6t ≤ -6. Then divide by 6: t ≤ -1.

The first step is usually to isolate the term with the variable by performing the opposite operation (addition or subtraction).

The inequality sign flips when you multiply or divide both sides by a negative number.

It is shown on a number line with an open or closed circle indicating whether the endpoint is included or excluded.