# Inequalities

Statements using <, >, or the signs for 'less than or equal' and 'more than or equal' that show a range of possible values.

Maths (school) · Part 03: Equations and formulae · Card 4 of 8 · Last updated 2026-10-19

## Analogy

Like a height rule on a fairground ride: anyone at least 1.2 m can ride, so there are many valid heights.

## Example

**2x + 3 < 11**

2x < 8
x < 4
So x can be 3, 2, 1, 0, ...

## In practice

A lift sign saying 'maximum 8 people' means the number of people must be 8 or fewer.

## Practice

### Flashcards

- **Solve 2x + 3 < 11.** x < 4.
- **When do you flip an inequality sign?** When you multiply or divide both sides by a negative number.

## Questions people ask

### When do you flip the inequality sign?

Flip the sign when you multiply or divide both sides by a negative number. For -2x < 8, dividing by -2 gives x > -4, not x < -4. In all other steps, the sign stays the same. Test it: x = 0 gives 0 < 8, which is true.

### How do you show an inequality on a number line?

Draw an open circle for < or >, because the end number is not included. Draw a filled circle for the 'or equal to' signs. Then shade the line in the direction of the allowed values. For x < 4, shade left from an open circle at 4.

## 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)
- [Simultaneous equations](https://studyvisually.com/learn/science/maths-school/maths-school-part-3/maths-school-part-3-concept-5)

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