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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. 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.