Undo a single operation to find the unknown, and check the answer by substituting it back in. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
An equation is a balance. Whatever you do to one side, do to the other, and the two sides stay equal. x−8=3 needs +8 on both sides, so x=11. 6a=42 needs ÷6, so a=7. 5y=3 needs ×5, so y=15.
The inverse of the operation sitting on the letter is the move you make. A number next to a letter is multiply (6a). A letter on the bottom of a fraction is divide. Do not swap the sides of a subtraction without changing the sign: from 8−x=3, adding x then subtracting 3 is safer than guessing.
Check by substituting your answer back. If x=11 then 11−8 really is 3. A failed check means the inverse was applied the wrong way, not that the question is broken.
Objectives
An equation says both sides are worth the same.
In x + 7 = 12, subtract 7 from both sides. That gives x = 5.
In 4x = 20, divide both sides by 4.
Key points
Solve equations of the form x+a=b and x−a=b.
Solve equations of the form ax=b and ax=b.
Solve equations where the unknown is being subtracted, such as 12−x=5.
Give answers that are negative, decimals or fractions when the numbers do not work out to whole numbers.
Worked examples
Example 1
Solve x + 2 = 4.
2 marks
To undo + 2, subtract 2 from both sides: x = 4 − 2.
x = 2.
Check: 2 + 2 = 4, so x = 2 is correct.
Answer: 2
Common slips
Slip: To undo + 4, subtract 2 from both sides: x = 4 − 2. That changes a number from the question, so it answers a different question.
Slip: x = 5. That changes a number in the working, so the step no longer follows from the one before.
Slip: Check: 6 + 2 = 4, so x = 2 is correct. That does not match the working above it.
Example 2
Solve 3x = 9.
2 marks
3x means 3 × x. Divide both sides by 3: x = 9 ÷ 3.
x = 3.
Check: 3 × 3 = 9, so x = 3 is correct.
Answer: 3
Common slips
Slip: 5x means 3 × x. Divide both sides by 3: x = 9 ÷ 3. That changes a number from the question, so it answers a different question.
Slip: x = 6. That changes a number in the working, so the step no longer follows from the one before.
Slip: Check: 7 × 3 = 9, so x = 3 is correct. That does not match the working above it.
Example 3
Solve x ÷ 4 = 4.
2 marks
To undo ÷ 4, multiply both sides by 4: x = 4 × 4.
x = 16.
Check: 16 ÷ 4 = 4, so x = 16 is correct.
Answer: 16
Common slips
Slip: To undo ÷ 6, multiply both sides by 4: x = 4 × 4. That changes a number from the question, so it answers a different question.
Slip: x = 19. That changes a number in the working, so the step no longer follows from the one before.
Slip: Check: 20 ÷ 4 = 4, so x = 16 is correct. That does not match the working above it.
Questions and answers
GCSE Maths solving one-step equations questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Solve x + 4 = 11.
Show answer
Answer: 7
Subtract 4 from both sides.
x = 11 − 4.
M1 — Subtract 4 from both sides.
A1 — Answer 7
Question 2 Easy2 marks
Solve x − 3 = 8.
Show answer
Answer: 11
Add 3 to both sides.
x = 8 + 3.
M1 — Add 3 to both sides.
A1 — Answer 11
Question 3 Medium2 marks
Solve x + 3 = 1.
Show answer
Answer: -2
Subtract 3 from both sides.
x = 1 − 3, which is negative.
M1 — Subtract 3 from both sides.
A1 — Answer -2
Question 4 Medium2 marks
A number is increased by 6 and becomes 20. What was the number?
Show answer
Answer: 14
Write it as x + 6 = 20.
Subtract 6 from both sides.
M1 — Write it as x + 6 = 20.
A1 — Answer 14
Question 5 Hard2 marks
Solve 4x = 10.
Show answer
Answer: 2.5
Divide both sides by 4.
The answer is not a whole number.
M1 — Divide both sides by 4.
A1 — Answer 2.5
Question 6 Hard2 marks
A number is decreased by 4 and becomes 9. What was the number?
Show answer
Answer: 13
Write it as x − 4 = 9.
Add 4 to both sides.
M1 — Write it as x − 4 = 9.
A1 — Answer 13
Question 7 Exam-style2 marks
Solve 4x = 14.
Show answer
Answer: 3.5
Divide both sides by 4.
The answer is not a whole number.
M1 — Divide both sides by 4.
A1 — Answer 3.5
Common mistakes
Most lost marks on this topic are one slip.
Subtracting the coefficient in 4x = 20.
Divide by 4.
Doing the inverse to one side only.
Both sides must stay equal.
Checking by doing the same step again.
Substitute the value into the original equation.
Spot the slip
Which operation undoes × 4?
÷ 4
− 4
+ 4
Show the slip
÷ 4 Division undoes multiplication.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write 'x =' on every answer line, not just a number.
Show the balancing step (e.g. '−9 from both sides') even when the answer is obvious — that is where the method mark sits in a 2-mark question.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.