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Solving linear equations

Free Printable Solving linear equations PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 3)

Download free solving linear equations worksheets (PDF), GCSE maths past paper questions and worked solutions for Solving linear equations (3P). This is a Grade 3 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Dr Frost, 1st Class Maths, Hannah Kettle, Maths4Everyone, Maths4EveryOne, Metatutor, Maths DIY, Maths Takeaway, Dr Austin, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our solving linear equations revision notes and worked examples with diagrams, try real GCSE past paper solving linear equations questions with step-by-step solutions, or download a PDF of all solving linear equations worksheet links.

Free Solving linear equations PDF Worksheets & Answers

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GCSE Maths Grade 3 Revision Notes & Method

Guide to Solving linear equations: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To solve a linear equation, use inverse operations on both sides of the equals sign to isolate the unknown letter x. If the equation contains brackets, expand them first. If there is a fraction, multiply both sides by the denominator to clear it.

When the unknown x appears on both sides of the equation, start by eliminating the smaller x term from both sides so that you keep a positive number of x's, then solve the remaining two-step equation.

Example 1: Solve 7x − 4 = 3x + 18

Solution:

Subtract 3x from both sides: 4x − 4 = 18
Add 4 to both sides: 4x = 22
Divide both sides by 4: x = 224 = 5.5
Answer: x = 5.5

Example 2: Solve 3(2x − 1)5 = 9

Solution:

Multiply both sides by 5: 3(2x − 1) = 45
Divide both sides by 3: 2x − 1 = 15
Add 1 to both sides: 2x = 16
Divide by 2: Answer: x = 8
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Solving linear equations Questions & Answers

Past Paper Example 1 GCSE Jun 2017 1F Q19 4 marks
(a) Solve 4(x – 5) = 18 (2) (b) –3 < t ⩽ 2, t is an integer. Write down all possible values of t. (2)
(a) Solve 4(x - 5) = 18 [2 marks]
(b) Write down all the possible values of t. [2 marks]
Worked Solution & Mark Scheme (4 marks)
Part (a) Solution:
4x – 20 = 18 M1
⇒ 4x = 38
⇒ x = 9.5 A1
Answer (a): x = 9.5
Part (b) Solution:
Integers strictly greater than –3 and up to 2: –2, –1, 0, 1, 2 M1 A1
Answer (b): –2, –1, 0, 1, 2
Past Paper Example 2 GCSE Nov 2017 2H Q1 3 marks
Solve 5x - 6 = 3(x - 1)
Worked Solution & Mark Scheme (3 marks)
5x – 6 = 3x – 3 M1
⇒ 2x = 3 M1
⇒ x = 1.5 (or 1 1/2) A1
Answer: x = 1.5
Past Paper Example 3 GCSE May 2024 1F Q17 3 marks
Solve 2(4x - 5) = 18
Worked Solution & Mark Scheme (3 marks)
8x – 10 = 18 M1
⇒ 8x = 28 M1
⇒ x = 28 ÷ 8 = 3.5 A1
Answer: x = 3.5

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