GCSE MATHS • HIGHER TIER

Basic Rearranging Made Simple

Use inverse operations to isolate a variable while keeping both sides of an equation balanced.

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Worked proofs

Basic Rearranging in Four Moves

1

Identify

Identify the variable you need to isolate.

2

Undo

Use the correct inverse operation.

3

Balance

Perform the same operation on both sides.

4

Check

Make sure the required variable is alone and check the result.

What You’ll Learn

Understand Rearranging

Know what it means to change the subject or isolate a variable.

Use Inverse Operations

Undo addition, subtraction, multiplication, division, powers and roots.

Keep Equations Balanced

Apply the same operation to both sides.

Solve Basic Rearrangements

Work confidently with simple addition, subtraction, multiplication and division equations.

Check Answers

Substitute an answer back into the original equation to verify it.

Key Rules

When rearranging equations, always do the same thing to both sides. This keeps the equation balanced and ensures the answer remains correct.

Worked Proof: Arc Length

Step-by-Step Method

  • 1. Identify the variable you want to isolate.
  • 2. Remove additions and subtractions first.
  • 3. Remove multiplications and divisions next.
  • 4. Remove powers or roots last.
  • 5. Check that the required variable is alone on one side.

More Worked Examples

1

Question: Make x the subject of x + 5 = 12

Subtract 5 from both sides

x = 12 − 5
x = 7

2

Question: Make x the subject of x − 8 = 10

Add 8 to both sides.

x = 18

3

Question: Make x the subject of 3x = 21

Divide both sides by 3

x = 7

4

Question: Make y the subject of y + 12 = 30

Subtract 12 from both sides.

y = 18
  • Common GCSE Mistakes
  • Balance: Do not perform an operation on only one side of the equation.
  • Inverse operation: Use the correct operation to undo the original one.
  • Signs: Take care with positive and negative values.
  • Working: Show each algebraic step clearly to reduce errors.
  • Exam Tips
  • Identify the variable you need to isolate before starting.
  • Use inverse operations one step at a time.
  • Do the same operation to both sides of the equation.
  • Write each step clearly so your method can be followed.
  • Check signs carefully, especially with subtraction.
  • Substitute your answer back into the original equation when possible.

Skills Used in Basic Rearranging

Inverse Operations

Equation Balance

Addition and Subtraction

Multiplication and Division

Substitution

Solving Equations

Algebraic Manipulation

Formula Rearrangement

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Frequently Asked Questions

Rearranging means changing an equation while keeping it balanced, usually so a particular variable is isolated.

Always do the same thing to both sides of the equation.

They are operations that undo each other, such as addition and subtraction or multiplication and division.

Multiply both sides by the divisor.

Substitute the answer back into the original equation and check that both sides are equal.

It provides the foundation for changing the subject of formulae and equations involving several variables.