GCSE MATHS • HIGHER TIER
One-Step Equations Made Simple
Learn how to solve one-step equations using inverse operations, keep equations balanced, and check your answers accurately.
Clear method
Exam practice
Worked proofs
One-Step Equations in Four Moves
1
Identify
Identify the operation being applied to the variable.
2
Inverse
Choose the inverse operation.
3
Balance
Apply the inverse operation to both sides.
4
Check
Substitute your answer into the original equation.
What You’ll Learn
Understand One-Step Equations
Recognise equations that require only one mathematical operation to solve.
Use Inverse Operations
Use the opposite operation to isolate the variable.
Keep Equations Balanced
Perform the same operation on both sides of the equation.
Solve Negative-Number Equations
Apply the same method carefully when negative values appear.
Check Solutions
Substitute the answer back into the original equation.
Key Rules
What Is a One-Step Equation?
A one-step equation is an equation that requires only one mathematical operation to solve. The goal is to find the value of the unknown variable.
Visual Example
x + 5 = 12
To solve:
Subtract 5 from both sides.
x = 7
Why Are One-Step Equations Important?
One-step equations teach the fundamental principle of balancing equations. Whatever operation is performed on one side of the equation must also be performed on the other side.
The Golden Rule of Equations
An equation is like a balance scale. If you add, subtract, multiply or divide one side, you must do exactly the same to the other side.
Worked Proof: One-Step Equations
Step-by-Step Method
- 1. Identify the operation.
- 2. Use the inverse operation.
- 3. Apply it to both sides.
- 4. Check your answer.
More Worked Examples
1
Solve: x + 8 = 15
Subtract 8 from both sides.
x = 7
2
Solve: x - 4 = 10
Add 4 to both sides
x = 14
3
Solve: 3x = 21
Divide both sides by 3.
x = 7
4
Solve: x/5 = 9
Multiply both sides by 5
x = 45
- Common GCSE Mistakes
- Wrong inverse: Use the operation that undoes the original one.
- One side only: Apply the operation to both sides.
- Arithmetic errors: Check each calculation carefully.
- No check: Substitute the answer into the original equation.
- Exam Tips
- Identify the operation first: Then choose its inverse.
- Keep both sides balanced: Do the same thing to each side.
- Show one clear step: Keep your working easy to follow.
- Watch negative numbers: Check signs carefully.
- Check by substitution: Confirm the equation is true.
Skills Used in One-Step Equations
Two-Step Equations
Expanding Brackets
Collecting Like Terms
Rearranging Formulae
Simultaneous Equations
Quadratic 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 One-Step Equations Tutorial
Step-by-step walkthroughs of One-Step Equations with clear methods and exam tips.
Frequently Asked Questions
A one-step equation requires only one mathematical operation to find the unknown value.
Inverse operations undo each other, such as addition and subtraction or multiplication and division.
Because the equation must remain balanced and both sides must stay equal.
Divide both sides by 3 to get x = 7.
Multiply both sides by 5 to get x = 45.
Substitute your answer into the original equation and check that both sides are equal.
