Multi-Step Inequalities

Multi-Step Inequalities

Multi-step inequalities are solved much like multi-step equations, with one extra rule: if you multiply or divide by a negative number, the inequality sign must reverse.

1) Simplify both sides

Distribute first, then combine like terms on each side if needed. This makes the inequality easier to isolate.

2) Move variable terms to one side

Use addition or subtraction to get all terms with the variable on one side and constants on the other. Keep the inequality sign unchanged when adding or subtracting the same value from both sides.

3) Isolate the variable

Use inverse operations to solve for the variable. If you divide or multiply by a positive number, the sign stays the same. If you divide or multiply by a negative number, reverse the sign.

4) Write the simplified answer

Your final answer should be in simplest form. If the solution is a compound inequality or interval, write it clearly.

5) Check your work

Substitute a value from your solution into the original inequality. The statement should be true. If the inequality involved a negative multiplication or division, double-check that the sign was flipped correctly.