Inequalities
Year 9 📊 Algebra Solve and represent inequalities on a number line.
📊 Inequality Symbols
Inequalities compare two expressions and show which is larger (or if they could be equal).
| Symbol | Meaning | Example |
|---|---|---|
| $<$ | Less than | $x < 5$ |
| $>$ | Greater than | $x > -2$ |
| $\leq$ | Less than or equal to | $x \leq 3$ |
| $\geq$ | Greater than or equal to | $x \geq 0$ |
🔧 Solving Linear Inequalities
Solve inequalities using the same methods as equations, with one crucial rule.
⚡ Critical Rule
When you multiply or divide both sides by a negative number, the inequality sign flips direction.Example: Solve $3x - 5 > 10$ → add 5: $3x > 15$ → divide by 3: $x > 5$
Example: Solve $-2x \leq 8$ → divide by $-2$ and flip: $x \geq -4$
📈 Showing Solutions
On a number line: open circle ○ for strict ($<$, $>$), filled circle ● for $\leq$, $\geq$. On a graph, shade the required region.
Number line: $x > 2$ — open circle at 2, arrow pointing right. $1 \leq x < 4$ — filled circle at 1, open circle at 4, line between them.
For graphical inequalities, use a dashed boundary line for strict inequalities ($<$, $>$) and a solid line for $\leq$, $\geq$.
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Inequalities
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Interactive demonstration available in the Calculator tab!
📊 Inequality Solver
Solve linear inequalities of the form ax + b OP c.