Two-Step Inequalities

Two-step inequalities

A two-step inequality is solved in much the same way as a two-step equation, but you must keep the inequality balanced. The goal is to isolate the variable while remembering that the inequality sign may need to change direction.

Method

1. Undo addition or subtraction first. Move the constant term to the other side by using the opposite operation.
2. Undo multiplication or division last. Divide or multiply both sides by the coefficient of the variable.
3. Reverse the inequality sign if needed. If you multiply or divide by a negative number, flip the sign: < becomes >, and ≤ becomes ≥.
4. Simplify the result. Write the variable alone with the inequality symbol in its correct direction.

Check your answer

Substitute a value from your solution into the original inequality. If the statement is true, your answer is likely correct. It is also helpful to test a value just outside the solution to make sure the inequality boundary works as expected.

Common mistake to avoid

Do not change the inequality sign when adding or subtracting the same number on both sides. Only reverse it when multiplying or dividing by a negative number.