Edexcel International GCSE Mathematics A · 4MA1
Linear inequalities
An inequality describes a set of possible values rather than a single solution. Most equation operations still work, but multiplication or division by a negative number reverses the comparison. Number lines distinguish included endpoints from excluded endpoints.
Key method
Keep the inequality balanced. Use an open circle for < or > and a filled circle for ≤ or ≥ when drawing a number line.
Worked example
Solve 7 − 2x > 1.
- Subtract 7 from both sides: −2x > −6.
- Divide by −2 and reverse the sign: x < 3.
- Check x = 2: 7 − 4 = 3, which is greater than 1.
Answer and interpretation
x < 3, shown by an open endpoint at 3 and a line extending left.
Common mistake
Keeping > after dividing by −2 gives the opposite solution set.
Practise independently
List the integer solutions of 1 ≤ 2x − 1 < 7.
Check your answer
2 ≤ 2x < 8, so 1 ≤ x < 4. Integers: 1, 2, 3.
Syllabus connection
This lesson develops linear inequalities within the algebra area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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