A linear inequality is like a linear equation but uses $<$, $\leq$, $>$, or $\geq$ instead of $=$. Solve using the same operations as equations, with one important extra rule.
Rule: when you multiply or divide by a negative number, the inequality sign reverses.
$$-2x > 6 \implies x < -3$$
Example: Solve $3x - 4 \leq 14$ $$3x \leq 18 \implies x \leq 6$$
Number lines: show solutions using:
- Open circle (○) for $<$ or $>$ (not included)
- Closed circle (●) for $\leq$ or $\geq$ (included)
Integer solutions: list all integers satisfying the inequality. For $-2 < x \leq 4$: integers are $-1, 0, 1, 2, 3, 4$.
Graphical representation: shade regions on a graph. Use a dashed line for strict inequalities and a solid line for $\leq$ or $\geq$.
Common error: forgetting to reverse the inequality sign when dividing by a negative number.