Compound inequalities
A standard method from Inequalities and linear programming: the steps and worked examples.
Steps
- Solve each part separately.
- Draw both on one number line.
- "and": the overlap only. "or": everything covered by either part.
Worked examples
Example 1: Compound inequalities: solve 2x − 1 < 5 and 3 − x ≤ 4.
2x − 1 < 5 → x < 3
3 − x ≤ 4 → x ≥ −1
"and": −1 ≤ x < 3For the whole topic, read Inequalities and linear programming: key points, common mistakes and how the DSE tests it.