Inequalities

Inequalities show relationships between expressions that aren't necessarily equal. While equations use the = symbol, inequalities use comparison symbols like < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

When solving inequalities, you can use the same basic operations as with equations—add, subtract, multiply, and divide on both sides. But here's a critical rule to remember: whenever you multiply or divide by a negative number, you must flip the inequality symbol. For example, when solving -3h > 15, dividing both sides by -3 gives you h < -5 (notice how > became <).

Graphing inequalities requires a number line and specific notation. Use an open circle for strict inequalities (< or >) to show the endpoint isn't included, and a filled circle for non-strict inequalities (≤ or ≥) to show the endpoint is included. Then draw an arrow pointing right for "greater than" expressions or left for "less than" expressions.

Remember: The direction of your arrow always follows the direction the inequality "opens" toward—right for greater than, left for less than!