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Linear inequalities — KCSE Mathematics

KCSE Mathematics · 111 practice questions · 4 syllabus objectives

37 easy38 medium36 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Solve linear inequalities in one variable and represent solutions on a number line using interval notation

Solve compound inequalities (a < x < b) and inequalities involving absolute values

Solve linear inequalities in two variables and represent the solution region graphically (shading)

Linear inequalities

Sample Questions

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1
easySHORT ANSWER3 marks

State the solution set for the inequality 5x + 3 < 2x + 12 and provide the answer in interval notation. [3 marks]

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Part (a) — 3 marks
Rearrange to form 5x - 2x < 12 - 3 (1 mk)
Simplify to obtain 3x < 9 (1 mk)
Divide by 3 to find x < 3; express in interval notation: (-∞, 3) (1 mk)
2
easySHORT ANSWER3 marks

Name the solution set for the inequality 3x + 5 < 2x + 10. (3 marks)

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Part (a) — 3 marks
Rearrange to get x < 5 (1 mk)
Identify the solution set as x ∈ (-∞, 5) (1 mk)
State that the solution is all x values less than 5 (1 mk)
3
easySHORT ANSWER3 marks

Explain how to solve the inequality 2x - 3 < 5 and identify the values of x that satisfy the inequality. (3 marks)

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Part (a) — 2 marks
Add 3 to both sides to get 2x < 8 (1 mk)
Divide both sides by 2 to find x < 4 (1 mk)
Part (b) — 1 mark
The solution set is all values of x less than 4 (1 mk)
4

State the solution set for the inequality |2x - 3| < 5, and explain your reasoning. (3 marks)

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Why Practise Linear inequalities?

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