Linear Inequalities for IGCSE Maths

What You Need to Know

Solving and representing linear inequalities on a number line. This subtopic is part of Inequalities in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding linear inequalities is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Linear Inequalities

Solving a linear inequality is almost identical to solving a linear equation, with one crucial difference: multiplying or dividing by a negative number reverses the inequality sign. Results are expressed as inequalities (e.g. x > 3) and represented on number lines with open circles for strict inequalities (< and >) and closed circles for ≤ and ≥. IGCSE 0580 Core and Extended both test this.

Step-by-Step Method

1. 1

   Treat it like an equation — almost

   Add, subtract, multiply, and divide as with an equation to isolate x.

2. 2

   REVERSE the sign when multiplying/dividing by a negative

   If you divide both sides by −3 to isolate x, the inequality flips: > becomes <, ≤ becomes ≥.

3. 3

   Write the solution as an inequality

   Express the answer as x > k, x ≤ k, etc. Do not write 'x = k'.

4. 4

   Represent on a number line

   Open circle (○) for < or >. Closed circle (●) for ≤ or ≥. Arrow pointing left for less than, right for greater than.

5. 5

   State integer solutions if asked

   List the whole number values of x that satisfy the inequality.

Exam Tips for Linear Inequalities

• The inequality sign flips ONLY when dividing or multiplying by a negative number — adding or subtracting does not change the sign.
• Use an open circle on the number line for strict inequalities (< and >) — a filled circle for ≤ and ≥.
• Do NOT write x = when expressing an inequality solution.
• After solving, substitute a value from the solution set back into the original to verify: if x > 3, test x = 5.

Practice Questions

Frequently Asked Questions