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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Variables Both Sides: Challenge & Extension

Subject: MathematicsGrade: GCSE Higher
Name:
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]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet