< Inequalities

Inequality Symbols

• < strictly less than — open circle on number line
• > strictly greater than — open circle
• ≤ less than or equal — closed (filled) circle
• ≥ greater than or equal — closed circle

Solving Is Like Equations — Except One Rule

Use the same inverse operations as equations. But there is one critical exception: when you multiply or divide both sides by a negative number, you must flip (reverse) the inequality symbol.

Example: −3x < 12. Divide by −3 and flip: x > −4.

Graphing on a Number Line

An inequality has infinitely many solutions — you graph them as a ray (half-line). Place an open circle at the boundary for < or >, and a closed circle for ≤ or ≥. Shade the region that satisfies the inequality.