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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.