Inequalities — Same Rules, One Exception

Solve inequalities exactly like equations with ONE critical rule:

THE RULE: When you multiply or divide by a NEGATIVE number, FLIP the inequality sign.

-2x > 10 becomes x < -5 (sign flipped)

Compound inequalities:

2 < 3x + 1 < 10

Subtract 1 from all parts: 1 < 3x < 9

Divide by 3: 1/3 < x < 3

Graphing:

Open circle = < or > (not including the endpoint)

Closed circle = le or ge (including the endpoint)

Systems of inequalities: The solution is the OVERLAPPING shaded region on a graph.

Desmos tip: Type the inequality directly. It shades the solution region for you.

Reference:

Wikipedia: Inequality

https://en.wikipedia.org/wiki/Inequality_(mathematics)