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Inequalities Practice Questions

KCSE (Kenya) · KCSE Mathematics · 146 free MCQs with instant results and detailed explanations.

146
Total
45
Easy
74
Medium
27
Hard

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Sample Questions from Inequalities

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Q1
Easy
Which of the following inequalities represents the statement: 'A number x is less than 7 but greater than 2'?
A. 2 < x < 7
B. x < 2 or x > 7
C. x > 7 and x < 2
D. x = 2 or x = 7
Show Answer & Explanation
Correct Answer: A
The inequality 2 < x < 7 correctly indicates that x is greater than 2 and less than 7, aligning with the given statement.
Q2
Easy
If 3x - 4 > 5, what is the value of x?
A. 3
B. 4
C. 5
D. 2
Show Answer & Explanation
Correct Answer: A
Solving the inequality 3x - 4 > 5 gives x > 3. Therefore, the smallest integer satisfying this is 4, but for the inequality, we check values greater than 3.
Q3
Easy
A student must score at least 50 marks to pass an exam. If the student's score is represented by s, which inequality represents this situation?
A. s >= 50
B. s < 50
C. s = 50
D. s > 50
Show Answer & Explanation
Correct Answer: A
The statement 'at least 50 marks' means that the score s must be 50 or more, which is correctly represented by s >= 50.
Q4
Medium
If 3x - 5 > 7, what is the range of x?
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Show Answer & Explanation
Correct Answer: A
To solve the inequality, first add 5 to both sides to get 3x > 12. Dividing by 3 gives x > 4, which is why option A is correct.
Q5
Medium
Solve the inequality: 2(x + 3) ≤ 4x - 6. What is the solution set?
A. x ≥ 3
B. x ≤ 3
C. x > 3
D. x < 3
Show Answer & Explanation
Correct Answer: B
Distributing 2 gives 2x + 6 ≤ 4x - 6. Rearranging leads to 12 ≤ 2x, or x ≥ 6, which means the solution set is x ≤ 3.
Q6
Medium
Which of the following is the solution to the inequality -5 < 2x + 3 ≤ 7?
A. x < 2
B. 0 < x ≤ 2
C. x > 2
D. x ≤ 2
Show Answer & Explanation
Correct Answer: B
Breaking the compound inequality leads to solving two parts: -5 < 2x + 3 gives x > 1 and 2x + 3 ≤ 7 gives x ≤ 2. Thus, the solution is 0 < x ≤ 2.
Q7
Medium
If |2x - 4| < 8, what are the possible values of x?
A. x < 3 or x > 7
B. x > 3 and x < 7
C. x > 1 and x < 5
D. x < 1 or x > 5
Show Answer & Explanation
Correct Answer: B
The absolute value inequality |2x - 4| < 8 leads to two inequalities: -8 < 2x - 4 < 8. Solving these gives the range 3 < x < 7.
Q8
Hard
If 3x - 5 < 7, what is the range of values for x?
A. x < 4
B. x > 4
C. x < 2
D. x > 2
Show Answer & Explanation
Correct Answer: A
To solve the inequality, add 5 to both sides to get 3x < 12, then divide both sides by 3, yielding x < 4. Therefore, the correct answer is A.
Q9
Hard
Solve the inequality 2(5 - x) > 3(x + 1). Which of the following represents the solution set?
A. x < 1
B. x > 1
C. x ≤ 1
D. x ≥ 1
Show Answer & Explanation
Correct Answer: A
Expanding the inequality gives 10 - 2x > 3x + 3. Rearranging leads to 7 > 5x, hence x < 1. Thus, the correct answer is A.
Q10
Hard
If 3x - 4 < 2x + 5, what is the range of values for x?
A. x < 9
B. x > 1
C. x < 1
D. x > 9
Show Answer & Explanation
Correct Answer: B
To solve the inequality, we first rearrange it: 3x - 2x < 5 + 4, leading to x < 9. This means x can take any value greater than 1, making option B correct.

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Inequalities — KCSE (Kenya) KCSE Mathematics Practice Questions Online

This page contains 146 practice MCQs for the chapter Inequalities in KCSE (Kenya) KCSE Mathematics. The questions are organized by difficulty — 45 easy, 74 medium, 27 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.