# Inequality and Compound Inequality

__Inequality:__

An *inequality* expresses the relative order of two mathematical expressions. The symbols (less than), (less than or equal to), (greater than), (greater than or equal to) are used to write inequalities.

__Note:__

The sign of an inequality is unchanged if it is multiplied or divided by a positive number.

For example,

Similarly,

__Note:__

The order of an inequality is reversed if it is multiplied or divided by a negative number.

For example,

Similarly,

__Linear Inequalities in One Variable:__

Inequalities of the form , , , , where , b are constant, and are called the *linear equalities in one variable* or first degree inequalities in one variable.

For example,

are all linear inequalities.

__Compound Inequality:__

A compound inequality is formed by joining two inequalities with a connective word such as “and” or “or.”

For example, and is a compound inequality.

__Note:__

If ‘x’ are the real numbers that satisfy the linear inequality then this is how we graph them:

The solution of inequality .

The graph of the solution of this inequality is given below.

The circle which marks 3 indicates that 3 is not included in the solution.

Now, the solution of inequality includes 3.

The graph of the solution of this inequality is given below.

The dot that marks 3 indicates that 3 is included in the solution of equality.