# Unknowns on both sides

When the letter appears on both sides, first move the letter terms to one side, then solve as normal.

Maths (school) · Part 03: Equations and formulae · Card 2 of 8 · Last updated 2026-10-19

## Analogy

Like two teams on a see-saw: take the same number of players off each side until one side has none.

## Example

**5x - 3 = 2x + 9**

Take 2x from both sides: 3x - 3 = 9
Add 3: 3x = 12
Divide by 3: x = 4

## In practice

Comparing two phone plans with different fixed fees and prices per minute gives an equation with x on both sides.

## Practice

### Flashcards

- **Solve 5x - 3 = 2x + 9.** x = 4. Subtract 2x, add 3, divide by 3.

## Questions people ask

### Which side should the x terms go on?

Either side works. Many people move them to the side where x has the larger number, so the answer stays positive. For 5x - 3 = 2x + 9, subtracting 2x leaves 3x on the left. Both choices give the same final answer.

### What if the equation has brackets?

Expand the brackets first, then collect the letter terms. For 2(x + 3) = x + 10, expanding gives 2x + 6 = x + 10. Take x from both sides: x + 6 = 10, so x = 4.

## Related concepts

- [Solving linear equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-1)
- [Changing the subject](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-3)
- [Inequalities](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-4)
- [Simultaneous equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-5)

Web page: https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-2
Study this card in the app: https://studyvisually.com/app/learn?category=maths-school&card=maths-school-part-3-concept-2