# Forming equations

Turning a worded problem into an equation by letting a letter stand for the unknown.

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

## Analogy

Like translating a sentence into a code you can solve.

## Example

**Double a number, add 7, get 21**

Let the number be x
2x + 7 = 21
2x = 14
x = 7

## In practice

Puzzles like 'I think of a number' use this skill, and so do real bills and budgets.

## Practice

### Flashcards

- **Turn 'double a number, add 7, get 21' into an equation.** 2x + 7 = 21, so x = 7.

## Questions people ask

### How do you start a worded algebra problem?

Choose a letter for the unknown and write down what it stands for. Then turn each phrase into maths: 'double' is 2 times, 'more than' is add, 'less than' is subtract. Build the equation, then solve it. Writing 'let x be the number of hours' makes your working clear, and examiners like seeing that step stated.

### Why should you check the answer in the words?

Checking in the original wording catches mistakes in forming the equation, not just in solving it. If x = 7, double is 14, add 7 gives 21. It matches the story, so the equation was set up correctly. It also shows whether the answer makes sense in real life.

## Related concepts

- [Solving linear equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-1)
- [Unknowns on both sides](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-2)
- [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)

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