In mathematics, an inequality is a relation between two values when they are different. Inequality means the condition of being unequal or lack of equality. Like x < y, x > y, x $\leq$ y etc. The sign ">" means is greater than, sign "<" means is less than. In each case the sign opens towards the larger number.
For example: 3 < 6 ("3 is less than 6") and
6 > 3 ("6 is greater than 3").

## What are Inequalities?

In general, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not. Inequality is actually an equation, we can solve it just like equations but it has no exact answer. We have two basic senses of inequalities as < and >.

• Open circle or round parenthesis denotes the number is not included.
• Closed circle or square parenthesis denotes the number is included.

Lets start with a one dimensional graph. It will contain only a one axis, say an x-axis. Here, we can consider two types of inequality:

• Simple Inequality
• Complex Inequality

### Simple Inequality:

This expression will contain only one inequality.

### Examples on Simple Inequality

Given below are some examples on simple inequality.

Example 1:

x < 7
According to this inequality, x will take all values less than 7. Also, as there is no equal sign, it means 7 is not included, so we use the open circle.

Example 2:

x $\geq$ -10
According to this inequality, x will take all the values greater than or equal to -10. Since there is an equal sign, -10 will be included, so we use a closed circle.

### Complex Inequality:

This expression will contain two inequalities. That is two conditions will be combined together.

### Examples on Complex Inequality

Given below are some examples on Complex Inequality.

Example 1:

2 $\leq$ x < 6

This means x will take values between 2 and 6. Here, 2 must be included, where as 6 will be excluded.

### Set Theory

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