11+ Maths · Topic explained
Equations: the balance idea
If x + 7 = 19, how do you find x?
The big idea
An equation is a balance: do the same to both sides and it stays level.
Picture it
Like a see-saw: take the same off both sides, or share both sides equally, and it stays balanced.
Key words
- equation
- Two things that are equal, with an = sign: 2x + 3 = 11.
- unknown
- The letter whose value you find.
- inverse
- The opposite operation: + undoes −, × undoes ÷.
- solve
- Find the value of the unknown.
Worked examples
- 1Warm-up
Solve x + 7 = 19
- Take 7 off both sides
- x = 19 − 7 = 12
- 211+ standard
Solve 4x − 5 = 23
- Add 5 to both sides: 4x = 28
- Divide both sides by 4: x = 7
- 311+ standard
Solve x ÷ 3 + 2 = 8
- Take 2 off both sides: x ÷ 3 = 6
- Multiply both sides by 3: x = 18
- 411+ standard
Solve 5x + 3 = 2x + 15
- Take 2x off both sides: 3x + 3 = 15
- Take 3 off both sides: 3x = 12
- Divide by 3: x = 4
The common mistake
The mistake
For 4x − 5 = 23, take 5 off: 4x = 18.
Instead
Undo '− 5' by adding 5: 4x = 28, so x = 7.
Why: Use the inverse: adding undoes taking away.
Where it comes up in the 11+
Solving equations, 'I think of a number' puzzles, and finding missing angles or lengths.
The video
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Equations: the balance idea worksheet
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Quick quiz
Have a go first, then tap to see the answer.
1. Solve 3x = 27.
- 9
- 24
- 30
- 81
Show the answerHide the answer
9
Divide both sides by 3: 27 ÷ 3 = 9.
2. Solve 2x + 9 = 25.
- 8
- 17
- 16
- 34
Show the answerHide the answer
8
2x = 25 − 9 = 16, so x = 8.
3. I think of a number, multiply it by 4 and take away 6. The answer is 30. What was my number?
- 6
- 9
- 24
- 36
Show the answerHide the answer
9
4n − 6 = 30, so 4n = 36 and n = 9.