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GCSE Equations Revision Guide
Master solving equations from basic one-step principles to complex algebraic fractions with our structured curriculum-aligned guide.
Foundation
Higher Tier
Exam Practice
Formulae
Topic Overview
Equations are the backbone of GCSE Mathematics. Whether you are calculating unknown lengths in geometry or determining the rate of a chemical reaction in science, the ability to manipulate and solve equations is a fundamental skill that underpins almost every quantitative subject.
This guide breaks down complex algebraic concepts into manageable chunks, ensuring you build a solid foundation before tackling the higher-tier challenges involving quadratic formulas and algebraic fractions.
Quick Navigation
Key Rules
Lesson Grid
Worked Examples
Resources
The Golden Rules of Equations
Rule 1: Keep it Balanced
Whatever operation you perform on one side of the equals sign, you MUST perform on the other. It's like a seesaw—equilibrium is everything.
Rule 2: Inverse Operations
Use the opposite operation to "undo" terms. Addition undoes subtraction, and multiplication undoes division. Work backwards step-by-step.
Lesson Modules
One-Step Equations
The fundamental building blocks using basic addition and subtraction.
Two-Step Equations
Combining multiplication and addition steps for more complex solutions.
Equations with Brackets
Learning how to expand and simplify before solving for the variable.
Equations with Fractions
Eliminating denominators to transform complex fractions into linear ones.
Core Subtopics
Structured lessons for every syllabus requirement.
Worked Example
Step-by-Step Walkthrough
THE QUESTION
Solve 3(x + 4) = 21
Method
- Expand the Bracket.
Multiply the 3 by both terms inside the bracket.
3x + 12 = 21 - Subtract 12.
Subtract 12 from both sides to isolate the term with x.
3x = 9 - Divide by 3.
Divide both sides by 3 to find the value of x.
x = 3
Common Mistake
Forgetting to multiply both terms inside the bracket (e.g. writing 3x + 4 = 21).
Final Answer
x = 3
Revision Resources
Worksheet
25 comprehensive practice questions for all levels.
Topic Quiz
10-minute timed quiz to test your speed and accuracy.
Exam Questions
Real past paper questions curated for current spec.
Mark Scheme
Step-by-step solutions to understand the scoring.
Playlist
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Expert Video Tutorials
Related Topics
Frequently Asked Questions
What is the difference between an expression and an equation?
An expression is a mathematical phrase without an equals sign (e.g., 2x + 5), while an equation always includes an equals sign (e.g., 2x + 5 = 11), stating that two expressions are equal.
When should I use the 'change side, change sign' rule?
This is a shortcut for the balancing rule. Use it when moving a term from one side of the equals sign to the other. For example, +5 on the left becomes -5 on the right.
How do I deal with x on both side?
The best strategy is to move the ‘smaller’ x term to the side with the ‘larger’ x term by using inverse operations. This keeps the coefficient of x positive and simplifies the process.
