Understand the rule first
An equation is like a balanced scale. Undo the final operation first and apply the same change to both sides.
Algebraic reasoning 11+ practice
Find an unknown by reversing operations while keeping an equation balanced.
Solve 4x + 7 = 31.
- Undo +7: 4x = 24.
- Undo ×4: x = 6.
- Check: 4 × 6 + 7 = 31.
A common misconception
Moving a number across the equals sign without understanding which inverse operation is needed.
Reusable method: Substitute the answer back into the original equation.Question 1 of 10 MathscoreSolve 5a = 45.
- Aa = 9
- Ba = 8
- Ca = 40
- Da = 50
Need a hint?
Undo multiplication by five.
Show worked answer
Answer A: a = 9
45 ÷ 5 = 9, so a = 9.
Quick method: Substitute the answer back into the original equation.
Question 2 of 10 MathscoreSolve 3b + 8 = 29.
- Ab = 5
- Bb = 9
- Cb = 11
- Db = 7
Need a hint?
Subtract eight before dividing by three.
Show worked answer
Answer D: b = 7
29 − 8 = 21; 21 ÷ 3 = 7.
Quick method: Substitute the answer back into the original equation.
Question 3 of 10 MathscoreWhen n = 6, what is 4n − 5?
- A14
- B24
- C29
- D19
Need a hint?
Replace n with six, then follow the operation order.
Show worked answer
Answer D: 19
4 × 6 − 5 = 24 − 5 = 19.
Quick method: Substitute the answer back into the original equation.
Question 4 of 10 Mathsexam-styleSolve 6c − 11 = 31.
- Ac = 6
- Bc = 20
- Cc = 42
- Dc = 7
Need a hint?
Undo minus eleven, then undo multiplication by six.
Show worked answer
Answer D: c = 7
31 + 11 = 42; 42 ÷ 6 = 7.
Quick method: Substitute the answer back into the original equation.
Question 5 of 10 Mathsexam-styleThree consecutive whole numbers total 72. What is the middle number?
- A23
- B24
- C25
- D36
Need a hint?
Represent the numbers as n − 1, n and n + 1.
Show worked answer
Answer B: 24
The outer changes cancel, so 3n = 72 and n = 24.
Quick method: Substitute the answer back into the original equation.
Question 6 of 10 MathscoreSolve 4x + 7 = 31.
- A5
- B6
- C7
- D9.5
Need a hint?
Subtract 7, then divide by 4.
Show worked answer
Answer B: 6
4x = 24, so x = 6.
Quick method: Substitute the answer back into the original equation.
Question 7 of 10 MathscoreSolve 3a − 5 = 2a + 9.
- A4
- B12
- C14
- D16
Need a hint?
Subtract 2a from both sides first.
Show worked answer
Answer C: 14
3a − 2a = 9 + 5, so a = 14.
Quick method: Substitute the answer back into the original equation.
Question 8 of 10 MathscoreFind the value of 2n² − 3 when n = 5.
- A22
- B35
- C44
- D47
Need a hint?
Square 5 before multiplying by 2.
Show worked answer
Answer D: 47
5² = 25; 2 × 25 − 3 = 50 − 3 = 47.
Quick method: Substitute the answer back into the original equation.
Question 9 of 10 MathsexamA rectangle has width x cm and length (x + 3) cm. Its perimeter is 30 cm. What is x?
- A6
- B5
- C7
- D9
Need a hint?
Write 2x + 2(x + 3) = 30.
Show worked answer
Answer A: 6
2x + 2x + 6 = 30, so 4x = 24 and x = 6.
Quick method: Substitute the answer back into the original equation.
Question 10 of 10 MathsstretchThree consecutive whole numbers have a total of 72. What is the largest number?
- A24
- B25
- C26
- D27
Need a hint?
The middle number is one third of the total.
Show worked answer
Answer B: 25
The middle number is 72 ÷ 3 = 24, so the numbers are 23, 24 and 25. The largest is 25.
Quick method: Substitute the answer back into the original equation.