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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. Addtion Property for Inequalities
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.