Worked example 1
3x + 5 = 20
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check: 3 × 5 + 5 = 20 ✓
Answer: x = 5
Maths · Intermediate
Solving linear equations step by step
An equation says two things are equal, such as 3x + 5 = 20. Solving it means finding the value of the letter that makes it true.
- 1Learn it
- 2See it worked
- 3Try it online
- 4Print it
- 5Check your answer
Before you start
Who it's for and what to know first
Negative numbers, the four operations and order of operations.
Learn it
How it works
- Think of a balance: whatever you do to one side, do to the other so it stays balanced.
- Use inverse (opposite) operations: + undoes −, × undoes ÷.
- Undo in reverse order. In 3x + 5, x was multiplied by 3 then 5 was added, so subtract 5 first, then divide by 3.
- Always check by substituting your answer back into the original equation.
Worked example 2
(y − 4) ÷ 2 = 7
- Multiply both sides by 2: y − 4 = 14.
- Add 4 to both sides: y = 18.
- Check: (18 − 4) ÷ 2 = 7 ✓
Answer: y = 18
Try it online · print it · check it
Practice questions
Tips
Common mistakes
- Doing an operation to only one side.
- Undoing in the wrong order (dividing before subtracting in 3x + 5 = 20).
- Sign errors with negatives — write each step on a new line.
Last reviewed: 25 September 2026