Grade 10 · Theory
Linear inequalities
Equations and inequalities · about 3 min
Visual overview: Linear inequalitiesAn inequality has a range of solutions rather than a single value, so the answer is an interval.
Key points- Solve exactly like an equation — with one exception.
- Multiplying or dividing by a NEGATIVE number reverses the inequality sign.
- Show the solution on a number line: open circle for < or >, closed circle for ≤ or ≥.
- Interval notation: x > 2 is (2; ∞), while −1 ≤ x < 4 is [−1; 4).
- Interval — a continuous set of solutions.
- Compound inequality — two conditions joined, e.g. −1 ≤ x < 4.
EXAM TIP
the sign flip when dividing by a negative is the single most common lost mark here — pause every time.