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.