Solving equations
Maths, Algebra. Usually met in years 7 to 10.
Solve linear equations by undoing each step, including equations with the unknown on both sides and with brackets.
What you practise
- One-step and two-step equations
- Unknowns on both sides
- Equations with brackets
Starts with x + a = b and finishes with a(x + b) = c. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Solve 8x = 72.
- x = 64
- x = 9
- x = 10
- x = 576
- x = 80
Show the answer and method
Answer: B, x = 9
The method: 8x means 8 × x. Divide both sides by 8: x = 72 ÷ 8 = 9.
Why the other options are wrong:
- A, x = 64: 8 was subtracted. Undo multiplying by 8 by dividing by 8.
- C, x = 10: Close, but check the division.
- D, x = 576: The right side was multiplied by 8 instead of divided.
- E, x = 80: 8 was added. Undo multiplying by 8 by dividing by 8.
Sample question, level 4 of 5
Solve 7x + 11 = x + 29.
- x = 3
- x = 6.667
- x = 18
- x = −3
- x = 2.25
Show the answer and method
Answer: A, x = 3
The method: Subtract 1x from both sides: 6x + 11 = 29. Subtract 11: 6x = 18. Divide by 6: x = 3.
Why the other options are wrong:
- B, x = 6.667: A sign went wrong when the numbers were moved across.
- C, x = 18: The x terms were collected, but the answer was not divided by 6.
- D, x = −3: The numbers were subtracted the wrong way round.
- E, x = 2.25: The x terms were added. To collect them, subtract 1x from both sides.
See where this fits: GCSE maths with AQA and Key Stage 3.
Related topics: Expanding brackets, Factorising quadratics, Sequences.
