Variables Both Sides: Problem Solving & Reasoning
Mathematics
GCSE Foundation
16 questions
~32 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on solving equations with variables on both sides, designed to develop procedural skills and reasoning for GCSE Foundation students.
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Variables Both Sides: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Read the key concept below before attempting the questions.
1.
When solving equations with variables on both sides, the goal is to collect like terms on one side and isolate the variable. This often involves adding or subtracting terms from both sides, then dividing to find the variable.
[2 marks]B
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: 4(2y - 1) = 3(y + 2)
[2 marks]3.
Solve for z: 5z - 3 = 2z + 6
[2 marks]4.
Solve for a: 2(a + 4) = 3(a - 2)
[2 marks]C
Targeted Practice on Variables Both Sides
Answer all questions. Show your working clearly.
1.
Solve for x: 7x + 2 = 3x + 14
[2 marks]2.
Solve for y: 6( y - 1) = 4( y + 2 )
[2 marks]3.
Solve for z: 2(3z + 5) = 4( z - 1)
[2 marks]4.
Solve for a: 5(a - 3) = 2(a + 4)
[2 marks]5.
Solve for x: 4x - 7 = x + 8
[2 marks]D
Real-World Applications
Answer all questions. Show your reasoning in the grid.
1.
A shop sells pencils for £2 each. If the total cost for x pencils is £14, write and solve an equation with variables on both sides to find x.
[3 marks]2.
A rectangle's length is 3 meters more than twice its width. If the perimeter is 26 meters, write and solve an equation to find the width.
[3 marks]E
Challenge & Extension
Attempt these more challenging problems involving variables on both sides.
1.
Solve for x: 2(3x + 4) - 5 = 4(x - 1) + 6
[3 marks]2.
Solve for y: 5( y + 2 ) - 3( y - 4 ) = 2( y + 1 ) + 8
[3 marks]F
Mixed Review & Error Analysis
Attempt these questions to review your understanding and identify mistakes.
1.
A student solves the equation 3x + 4 = 2x + 7 by subtracting 2x from both sides, then dividing both sides by 1. Is their method correct? Explain and correct it if needed.
[3 marks]2.
Solve for x: 4x + 3 = 4x + 5. Identify the mistake in solving this equation.
[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