GCSE MATHS • HIGHER TIER
Equations with Brackets Made Simple
Learn how to expand brackets, collect like terms, solve linear equations and check solutions accurately.
Clear method
Exam practice
Worked proofs
Equations with Brackets in Four Moves
1
Expand
Multiply through the brackets carefully.
2
Simplify
Collect like terms where needed..
3
Solve
Move variables and numbers to opposite sides and solve..
4
Check
Substitute your answer into the original equation
What You’ll Learn
Understand Bracket Equations
Recognise equations that must be expanded before solving.
Expand Brackets
Multiply every term inside the bracket correctly.
Collect Like Terms
Simplify expressions before solving.
Solve Linear Equations
Use inverse operations to isolate the unknown.
Check Solutions
Substitute answers back into the original equation.
Key Rules
What Are Equations with Brackets?
Equations with brackets contain one or more brackets that must be expanded before the equation can be solved. In most cases, the first step is to remove the brackets by multiplying through.
Visual Example
2(x + 3) = 14
Expand first:
2x + 6 = 14
Then solve the equation.
Why Are Equations with Brackets Important?
These equations combine multiple GCSE Algebra skills. Students must be able to expand brackets correctly before applying equation-solving methods.
Worked Proof: Equations with Brackets
Step-by-Step Method
- 1. Expand the brackets.
- 2. Collect like terms if needed.
- 3. Move variables to one side.
- 4. Move numbers to the other side.
- 5. Solve the equation.
- 6. Check your answer.
More Worked Examples
1
Solve 2(x + 4) = 18.
2x + 8 = 18
2x = 10
x = 5
x = 5
2
Solve 3(x + 2) = 21.
3x + 6 = 21
3x = 15
3
Solve 4(x - 1) = 20.
4x - 4 = 20
4x = 24
4
Solve 5(x + 3) = 2x + 21.
5x + 15 = 2x + 21
3x + 15 = 21
3x = 6
3x = 6
- Common GCSE Mistakes
- Skipping expansion: Expand the brackets before solving.
- One-term multiplication: Multiply every term inside the bracket.
- Sign errors: Take extra care with negative brackets.
- Like terms: Simplify like terms before solving.
- Arithmetic errors: Check each inverse operation carefully.
- Exam Tips
- Expand first: Remove brackets before rearranging.
- Show each step: Keep the algebra easy to follow.
- Watch signs: Negative multipliers change every term.
- Collect like terms: Simplify before isolating x.
- Check by substitution: Put your answer back into the original equation.
Skills Used in Equations with Brackets
Expanding Brackets
Collecting Like Terms
One-Step Equations
Two-Step Equations
Rearranging Formulae
Simultaneous Equations
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Equations with Brackets Tutorial
Step-by-step walkthroughs of Equations with Brackets with clear methods and exam tips.
Frequently Asked Questions
Expand the brackets by multiplying every term inside the bracket.
Collecting like terms simplifies the equation and makes it easier to solve.
A negative multiplier changes the sign of every term inside the bracket.
Yes. Move the variable terms to one side before solving.
Substitute your value into the original equation and check that both sides are equal.
Expanding brackets, collecting like terms and basic one-step and two-step equations.
