Linear Inequation: Linear inequality is an inequality which involves a linear function and it contains one of the symbols of inequality.

- is less than
- is greater than
- is less than or equal to
- is greater than or equal to
- is not equal to

A linear inequality actually looks exactly like a linear equation , with the inequality sign replacing the equality sign .

Two-dimensional linear inequalities are expressions in 2 variables of the form: where the inequalities may either be strict or not.

A statement of any of the following forms: where and are real numbers and is called a Linear Inequation in .

Replacement Set or Universal Set: This is a set which contains all the values of the variable , which would satisfy the inequation.

Solution Set: This is a subset of the replacement set which satisfy the given inequation.

Properties of Inequalities

__Addition and Subtraction Property: __A common constant c may be added to or subtracted from both sides of an inequality. For any real numbers

__Multiplication and Division Property:__ The property states that for any real numbers,

If , then multiplying or dividing by c does not change the inequality:

If , then multiplying or dividing by inverts the inequality:

__Transitive property__ of inequality states that for any real numbers :

__Converse Property__: The relations ≤ and ≥ are each other’s converse. For any real numbers

__Additive inverse:__ The properties for the additive inverse state: For any real numbers , negation inverts the inequality:

__Multiplicative Inverse__: The properties for the multiplicative inverse state:

For any non-zero real numbers that are both positive or both negative:

If anyone of is positive and the other is negative, then:

For any non-zero real numbers :