Variables Both Sides: Challenge & Extension
Mathematics
GCSE Higher
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet covering Multi-Step Equations with Variables Both Sides, designed for challenge and extension for GCSE Higher students.
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Full preview • 14 questions
Variables Both Sides: Challenge & Extension
Subject: MathematicsGrade: GCSE Higher
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Date:
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Untitled Worksheet
Grade GCSE Higher
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Solve for x: 3x + 5 = 2x + 9
[2 marks]2.
Solve for y: 7y - 3 = 4y + 6
[2 marks]3.
Solve for z: 2(3z - 4) = 5z + 2
[2 marks]4.
Simplify and solve: 5(2x + 3) - 4x = 3x + 12
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Provide explanations where necessary.
1.
A rectangle's length is 3 times its width. If the perimeter is 48 cm, find the length and width. Show your working.
[4 marks]2.
Solve for x: 4x - (2x + 5) = x + 7, and explain each step.
[4 marks]C
Real-world Applications
Answer all questions. Show your working clearly.
1.
A car rental company charges a fixed fee plus a cost per mile. If the total cost for x miles is given by C = 50 + 0.2x, find the number of miles when the total cost is $90. Show detailed working.
[3 marks]D
Challenge & Extension
Attempt these challenging problems. Show your detailed working.
1.
Solve for x: 2(3x - 4) = 4x + 6, then verify your solution.
[4 marks]2.
Construct an equation with variables on both sides that simplifies to x = 7. Show the steps involved.
[4 marks]E
Mixed Review
Answer all questions and check your answers carefully.
1.
Solve for y: 3(2y - 1) = y + 8
[2 marks]2.
If 5x + 2 = 3x + 8, what is x? Show your working.
[2 marks]3.
Construct a simple equation with variables on both sides that has no solution. Write the equation and explain why.
[3 marks]F
Error Analysis
Identify the mistake in each problem and correct it.
1.
A student solves 4x + 2 = 2x + 10 and gets x = 4, but their answer is incorrect. Find the mistake and correct it.
[3 marks]2.
A student writes: 3(y - 2) = 2y + 4, and solves to y=8, but this is wrong. Find the mistake and fix it.
[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
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet