inequality

An inequality is a way to compare two values or expressions that are not equal to each other. 

It is often used to compare numbers on the number line by their size.

Key Words & Symbols

greater than or more than - a value is bigger than another value.

less than - a value is smaller than another value.

least or at least - no less than a value, a minimum

most or at most - no more than a value, a maximum

Example 1

The number x can be any real number greater than -1. 

It can not be -1.

We use an open circle, because greater than means we can not be -1, so the open circle shows we are not allowed to be -1.

Example 2

The number x can be any real number greater than or equal to -1.

It can be -1. 

We use a closed circle, because greater than or equal to means we can be -1, so the closed circle shows we can include -1.

Example 3

The number x can be any real number less than 2. 

It can not be 2. 

We use an open circle, because less than means we can not be 2, so the open circle shows we are not allowed to be 2.

Example 4

The number x can be any real number less than or equal to 2. 

It can be 2. 

We use a closed circle, because less than or equal to means we can be 2, so the closed circle shows we can include 2.