# 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 reserved 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, 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:__

The real numbers ‘x’ which satisfy the linear inequality in one variable ‘x’ from its solution.

For example,

The solution of inequality

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

The hole marked on 3 indicates that 3 is not included in the solution.

Now, the solution of inequality included 3

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

The dark hole is marked on 3 indicating that 3 is included in the solution of equality.