GCSE-ready- Home
- Lessons
- KS3 Mathematics
- Solving linear equations
Solving linear equations
🎬 The doodle video for this lesson is coming soon. Subscribe on YouTube to see it first.
An equation is like a balance. Do the same thing to both sides and it stays balanced until the unknown is on its own.
The balance idea
To solve 3x + 4 = 19, undo the operations in reverse order.
Subtract 4 from both sides: 3x = 15
Divide both sides by 3: x = 5
Subtract 4 from both sides: 3x = 15
Divide both sides by 3: x = 5
Inverse operations
+ and − undo each other. × and ÷ undo each other.
x − 6 = 10 → add 6 → x = 16
x4 = 3 → multiply by 4 → x = 12
x − 6 = 10 → add 6 → x = 16
x4 = 3 → multiply by 4 → x = 12
Check your answer
Put your answer back into the equation.
x = 5 in 3x + 4: 3 × 5 + 4 = 19. Correct.
x = 5 in 3x + 4: 3 × 5 + 4 = 19. Correct.
Solve 3x − 5 = 16.
- Add 5 to both sides: 3x = 21
- Divide both sides by 3: x = 7
- Check: 3 × 7 − 5 = 16
Answer: x = 7
Use inverse operations on both sides: undo + and − first, then × and ÷. Always check by substituting back.
The interactive lesson includes the diagrams for this topic.
Check you have got it
Answer 7 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.