# Representing inequalities on number lines

**Inequalities**

In algebra, an **inequality** is a statement which involves the following symbols:

>, <, ≥, ≤

These meanings can be as follows:

*x* > 4, this means that *x* is **greater than** 4

*x* < -7, this means that *x* is **less than** -7

*x* ≥ 3, this means that *x* is **greater than or equal to** 3

*x* ≤ 11, this means that *x* is **less than or equal to** 11

These rules can than be taken further can combined into a single statement.

*x* > 5 **and** *x* ≤ 16 we can be written as

5 < *x *≤ 16

**Reversing inequalities**

Inequalities can either be read from left to right or from right to left. This is done by swapping the terms on either side of the inequality sign and reversing the sign.

For example,

*x* > *y* = *y* < *x
*

*x*≥

*y*=

*y*≤

*x*

**Representing inequalities on number lines**

Number lines is a tool used to represent the **solution set**.

The above example, can represent *x* > 2.

Note: represents that the number on top of it is not included and the arrow represents that the solution extends beyond the number line.

*x* ≤ 3 can be represented as:

Note: represents that the number on top of it is included and the arrow represents that the solution extends beyond the number line.

–1 ≤ *x* < 4 can be represented as:

**Integer solutions**

In situations where *x* can only be an integer (which can be positive or negative whole number) there can sometimes be only be a number of values.

For example, list the integer values for –2 < *x* ≤ 4

These are as follows: –1, 0, 1, 2, 3, 4