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Inequalities

Use the symbol  " < " or " > "  to express the relationship of less than or large than is called inequalities.

Example

What is an inequalities?

Less than

Any numbers less than one can be expressed as x < 1.

Example

How to express less than one in the number asix?

Large than

Any numbers large than zero can be expressed as x > 0

Example

How to express larger than zero in the number asix?

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

How to express less than or equal to one in the number asix?

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

How to express larger than or equal to zero in the number asix?

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.

 How to express large than p and less than q in the number asix?

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.

inequality example 1

Addtion property for Inequalities

If a < b, then a + c < b + c, in which a, b and c are real numbers.

Example

What is the addtion property for inequalities?

Subtraction property for Inequalities

If a < b, then a - c < b - c, in which a, b and c are real numbers.

Example

What is the subtraction property for inequalities?

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

What happend if multiply a possitive number for inequalities?

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

What happend if multiply a negative number for inequalities?

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

How to divide a positive number for inequalities?

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

How to divide a negative number for inequalities?

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

Example of one variable first degree inequalities.

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

Example of one variable first degree inequalities.
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.