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# Inequalities

Inequalities
Use the symbol  " < " or " > "  to express the relationship of less than or large than is called inequalities.
Example
Less Than
Any numbers less than one can be expressed as x < 1.
Example
Large Than
Any numbers large than zero can be expressed as x > 0
Example
Less Than or Equal To
Any numbers that are less than one or equal to one can be expressed as x < 1 or x = 1.
Example
Large Than or Equal To
Any numbers that are large than zero or equal to zero can be expressed as x > 0 or x = 0.
Example
Large Than p and Less Than q
Any numbers that are large than p and less than q can be expressed as x > p and x < q.
Example
If p = -1 and q = 2, then x > -1 and x < 2.
Large Than or Equal To p and Less Than or Equal To q
Any numbers that are large than or equal to p and less than or equal to q can be expressed as x >= p and x <= q.
Example
If p = -1 and q = 2, then x >= -1 and x <= 2.
If a < b, then a + c < b + c, in which a, b and c are real numbers.
Example
Subtraction Property for Inequalities
If a < b, then a - c < b - c, in which a, b and c are real numbers.
Example
Property of Multiplying of a Positive Number for Inequalities
If a < b, then a c < b c, in which a, b and c are real numbers and c is a positive number.
Example
Property of Multiplying a Negative Number for Inequalities
If a < b, then a c > b c, in which a, b and c are real numbers and c is a negative number.
Example
Property of Dividing a Positive Number for Inequalities
If a < b, then a / c < b / c, in which a, b and c are real numbers and c is a positive number.
Example
Property of Dividing a Negative Number for Inequalities
If a < b, then a / c > b / c, in which a, b and c are real numbers and c is a negative number.
Example
One Variable First Degree Inequalities
The inequalities in which there is only one variable with degree of one is called one variable first degree inequalities.
Example
Solution of One Variable First Degree Inequalities
If ax + b < 0, then x < -b/a (a is not zero). if ax + b > 0, then x > -b/a (a is not zero).
Example
Steps to Solve Inequalities
(1). Removing parenthesis.
(2). Moving all veriable terms to the left side of the inequality and moving all numerical terms to the right side of the inequality.
(3). Combining similar terms.
(4). Dividing by the coefficient of the variable on both side.
(5). If multiply -1 on both side, then the inequality will change its direction.