Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Algebra and Graphs
Inequalities
What is Inequalities?
A statement that one quantity is less than, greater than, or not more or less than another, whose solution is a range of values rather than a single value. Linear inequalities are solved by the same operations as equations, with one exception: multiplying or dividing both sides by a negative number reverses the direction of the inequality. In one variable the solution is an interval shown on a number line with open circles for strict inequalities and closed circles for inclusive ones; in two variables it is a region of the plane bounded by broken lines for strict inequalities and solid lines for inclusive ones.
This definition is part of the Algebra and Graphs chapter in Cambridge O Level Mathematics (Syllabus D).
Examiner tips on Inequalities
- Shade the unwanted region. This surprises students who have learned the opposite convention elsewhere, and it is stated explicitly in the syllabus. The practical reason is good: when three or four inequalities overlap, shading what you don't want leaves the answer as the one clear, unshaded patch, instead of an unreadable pile of overlapping shading. Always label that clear patch \(R\), and always read the question in case it directs otherwise.