IGCSE Math RevisionWorked example 1: Unknowns on both sides
Solve \(5x-7=2x+11\).
Solution
- Subtract \(2x\) from both sides: \(3x-7=11\).
- Add 7: \(3x=18\).
- Divide by 3: \(x=6\).
Answer: \(x=6\)
Tip: Check: 5 × 6 − 7 = 23 and 2 × 6 + 11 = 23.
Edexcel IGCSE Maths (4MA1) · Unit 3: Equations & Sequences
IGCSE Maths Linear Equations Questions and Answers
Linear Equations questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 6 worked examples first, then cover each solution and redo it yourself.
- 6 worked examples
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Solving linear equations & inequalities: Finding the unknown in equations and inequalities with one variable.
- Equations 1: Solving one-step linear equations.
- Equations 2: Two-step and bracket-first linear equations.
- Equations 3: Equations with the unknown on both sides.
- Equations 4: Linear equations containing fractions.
- Equations 5: Simultaneous linear equations by elimination.
Linear Equations worked examples
Worked example 2: Two-step equation
Solve \(\dfrac{x}{4}+3=7\).
Solution
- Subtract 3: \(\dfrac{x}{4}=4\).
- Multiply by 4: \(x=16\).
Answer: \(x=16\)
Tip: Undo the operations in reverse order.
Worked example 3: Brackets on both sides
Solve \(6(x-2)=2(x+8)\).
Solution
- Expand: \(6x-12=2x+16\).
- \(4x=28\), so \(x=7\).
Answer: \(x=7\)
Tip: Collect x terms on the side with more x.
Worked example 4: Equation with fractions
Solve \(\dfrac{x+5}{4}=\dfrac{2x-1}{3}\).
Solution
- Cross-multiply: \(3(x+5)=4(2x-1)\).
- \(3x+15=8x-4\), so \(19=5x\).
- \(x=\tfrac{19}{5}=3.8\).
Answer: \(x=3.8\)
Tip: Brackets keep the whole numerator together.
Worked example 5: Forming an equation
A triangle has sides \(x\), \(x+4\) and \(2x-1\) cm. Its perimeter is 31 cm. Find \(x\).
Solution
- \(x+(x+4)+(2x-1)=31\).
- \(4x+3=31\), so \(x=7\).
Answer: \(x=7\)
Tip: Define the unknown and write the equation in words first.
Worked example 6: Consecutive numbers
The sum of three consecutive even numbers is 138. Find the numbers.
Solution
- Let them be \(n\), \(n+2\), \(n+4\).
- \(3n+6=138\), so \(n=44\).
- The numbers are 44, 46, 48.
Answer: 44, 46, 48
Tip: Consecutive even numbers differ by 2.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise linear equations for the exam
- Unit 3 practice: Equations & Sequences in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test linear equations?
Either Higher tier paper, 1H or 2H, can test linear equations: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more linear equations questions?
In the IGCSE student hub: Unit 3 (Equations & Sequences) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.