Mastering Inequalities
Mathematics
GCSE Foundation
1 questions
~2 mins
0 views0 downloads
About This Worksheet
A worksheet covering Inequalities for GCSE Foundation students, focusing on algebraic inequalities and their applications.
Topics covered:
Worksheet Preview
Full preview • 1 questions
Mastering Inequalities
Subject: MathematicsGrade: GCSE Foundation
Name:
Date:
Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the brief explanation below before attempting the questions.
1.
An inequality shows the relationship between two expressions where one is greater than, less than, or equal to the other. For example, x + 3 > 7. Understanding how to solve and represent inequalities is essential in algebra.
[2 marks]B
Procedural / Fluency Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Solve for x: 2x - 5 > 9.
[2 marks]2.
Solve the inequality: 3x + 4 ≤ 16.
[2 marks]3.
Express the inequality: x/2 < 5 in words.
[2 marks]4.
Determine the solution set for: 5 - 2x > 1.
[2 marks]5.
Solve: -x + 3 ≥ 7.
[2 marks]C
Reasoning and Application Questions
Answer all questions. Show your reasoning in the grid spaces provided.
1.
If x + 2 < 5, what is the range of possible values for x? Illustrate on a number line.
[3 marks]2.
A rectangle has a length that is greater than its width by 4 units. If the width is less than 7 units, what is the possible range for the length? Show your working.
[4 marks]3.
Solve the inequality: 2(3x - 4) ≤ 8, and interpret the solution in context.
[3 marks]4.
A shop offers a discount on a jacket such that the final price is less than $50. If the original price is p dollars and the discount is 20%, write an inequality for p and solve for p.
[4 marks]5.
The inequality x/3 + 2 > 4 represents a situation. What is the smallest possible value of x? Show your working.
[3 marks]D
Challenge / Real-world Word Problems
Attempt these challenging problems. Show detailed working.
1.
A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If the total cost c is less than $100, find the maximum number of miles the car can be driven. Write and solve an inequality to find your answer.
[4 marks]2.
A student’s test scores are represented by the inequality 70 ≤ x ≤ 100. If the student needs to score at least 75 to pass, what is the minimum score they can get? Provide reasoning and solution.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Related Worksheets
Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet