# Introduction to Inequalities

**Inequality** tells us about the **relative size** of values.

Mathematics is not always about "equals", sometimes we only know that something is greater or less than.

### Example: Alex and Billy have a race, and Billy wins!

What do we know?

We don't know **how fast** they ran, but we do know that Billy was faster than Alex:

Billy was faster than Alex

We can write that down like this:

b > a

(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

We call things like that **inequalities** (because they are not "equal")

## Greater or Less Than

The two most common inequalities are:

Symbol |
Words |
Example Use |
---|---|---|

> |
greater than |
5 > 2 |

< |
less than |
7 < 9 |

They are easy to remember: the "small" end always points to the smaller number, like this:

Greater Than Symbol: **BIG > small**

### Example: Alex plays in the under 15s soccer. How old is Alex?

We don't know **exactly** how old Alex is, because it doesn't say "equals"

But we **do know** "less than 15", so we can write:

Age < 15

The small end points to "Age" because the age is smaller than 15.

## ... Or Equal To!

We can also have inequalities that include "equals", like:

Symbol |
Words |
Example Use |
---|---|---|

≥ |
greater than or equal to |
x ≥ 1 |

≤ |
less than or equal to |
y ≤ 3 |

### Example: you must be 13 or older to watch a movie.

The "inequality" is between **your age** and the **age of 13**.

Your age must be "greater than **or** equal to 13", which is written:

Age ≥ 13

## Comparing Values

Practice >, < and = with Compare Numbers to 10

Learn more about Inequalities at Less Than or Greater Than