GCSE Maths • Foundation & Higher
GCSE Equations Revision Guide
Keep both sides balanced and isolate the unknown one clear step at a time.
Foundation
Exam practice
Worked examples
What You'll Learn
Understand Equality
Interpret the equals sign as a balance between two expressions.
Solve One-Step Equations
Undo one operation using its inverse.
Solve Two-Step Equations
Reverse operations in a sensible order and isolate the unknown.
Solve Equations with Brackets
Expand every term, simplify and solve.
Solve Equations with Fractions
Clear denominators using a suitable common multiple.
Check and Interpret Solutions
Substitute answers and recognise one, none or infinitely many solutions.
Key Rules
Lessons Modules
One Step Equations
Use one inverse operation and check by substitution.
Two Step Equations
Undo two operations in sequence and keep the equation balanced.
Equations With Brackets
Expand, simplify and solve equations containing brackets.
Equations With Fractions
Clear one or several denominators before solving.
Core Subtopics
Worked Examples
Equation with Brackets and Fractions
QUESTION
Solve (2x−1)/3 + (x+2)/2 = 7.
- Given information: The denominators are 3 and 2, so their lowest common multiple is 6.
- Method: Multiply every term by 6, expand, collect like terms and isolate x.
- Multiply throughout by 6: 2(2x−1)+3(x+2)=42.
- Expand both brackets: 4x−2+3x+6=42.
- Collect like terms: 7x+4=42.
- Subtract 4 from both sides: 7x=38.
- Divide by 7: x=38/7.
- Check in the original: (2(38/7)−1)/3 + ((38/7)+2)/2 = 23/7 + 26/7 = 49/7 = 7.
- Final answer: x=38/7.
- Independent answer check: Substitution gives 7 on the left, matching the right-hand side.
- One common mistake: When multiplying by 6, multiply every complete term, including both fractional terms and the right-hand side.
- Common GCSE Mistakes
- Changing Only One Side
- Treating the Equals Sign as an Instruction
- Using the Wrong Inverse
- Dividing Before Removing the Constant
- Expanding Only the First Term
- Losing a Negative Sign
- Moving Terms Without Explaining Signs
- Clearing Only Some Fractions
- Dividing by the Denominator Incorrectly
- Rounding an Exact Fraction
- Checking a Rearranged Line Only
- Exam Tips
- Write one algebraic change per line so the method is easy to follow.
- Use balance operations rather than unexplained “moving” of terms.
- Circle or underline the term you intend to undo first.
- When brackets appear, expand carefully before collecting like terms.
- For several denominators, write the LCM before multiplying every term.
- Keep fractions exact during working.
- Check negative coefficients and subtraction signs before dividing.
- Substitute the solution into the original equation and compare both sides.
- In a word problem, define the unknown, form the equation, solve it and answer in context.
Ready to Practice?
Printable Worksheet
Progress from one-step equations to brackets and fractions.
Interactive Quiz
Choose inverse operations and diagnose common errors.
Exam-Style Questions
Form and solve multi-step equations in context.
Watch the Equations Tutorial
Equations with Brackets , Equations with Fractions
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Frequently Asked Questions
A mathematical statement saying that two expressions have equal value.
Finding every value of the unknown that makes the original equation true.
Because equal quantities remain equal only when the same valid operation is applied to both.
An operation that undoes another, such as subtraction undoing addition.
Usually yes. Expand every term, simplify, then solve the resulting equation.
Multiply every term on both sides by a common multiple of the denominators, preferably the LCM.
Yes. Leave it as an exact fraction unless a decimal or rounding is requested.
Substitute it into the original equation and verify that both sides are equal.
Yes. If simplifying produces a false statement such as 0=5, there is no solution.
Yes. If both sides simplify to the same expression, the equation is an identity and has infinitely many solutions.
