An inequality is a statement that two expressions are not equal.

**a < b**means that a is less than b.

**a > b**means that a is greater than b.

**a ≠ b**means that a is not equal to b

**a ≤ b**means that a is less than or equal to b The notation

**a ≥ b**means that a is greater than or equal to b

Inequality Statement |
Equation |

x is at least 3 | x ≥ 3 |

y is at most 9 | y <= 9 |

z is between 2 and 4 | 2 < z < 4 |

x is less than 3 | X < 3 |

y is more than 9 | Y > 9 |

You can solve inequalities in the same way you can solve equations, by following these rules:

**included**” we draw a

**solid circle**, as the start point.

**not included**” we draw an

**empty circle**, as the start point.

**X ≥ 4**, means that X can equal any number greater than or equal to 4 (the value of X could be

**4, 5, 6, 7, 8,**and so on). This is an example of an unbounded set, the set of all numbers greater than or equal to 4. The closed circle in the graph indicates that 4 is a member of the solution set.

**Bounded Inequalities**.

**X ≥ 1 and X ≤6**

(the value of X could be 1, 2, 3, 4, 5, or 6)

__Inequalities__

### Graphing Inequalities

### Properties of Inequalities

### Representing Inequalities on a Number Line

### Inequalities on a Number Line

### Reversal Property of Inequality

### Solving and Graphing Linear Inequalities

### Double Inequalities (a<X<b)

### Double Inequalities (a<X<b) 2

__IQ02 __Linear_Inequalities

__IQ03 __One_Step_Inequalities

__IQ04 __Two_Step_Inequalities

__IQ01 __Inequalities_Word Problems

**Inequalities Properties (Help)**

## Graphing Inequalities on Number Lines.

The graph of a linear inequality in one variable is a number line. When we graph an inequality on a number line we use open and closed circles to represent the number. The open circle means the number is not included in the solution

**X>5** means that whatever value *x* has, it **must be greater than 5.** The open dot shows that 5 is not a solution. Numbers greater than 5 are to the right of 5 on the number line.

The closed circle means the number is included in the solution. X ≥ 5 means that whatever value *x* has, it must be greater than or equal to 5

Numbers less than 5 are to the left of 5 on the number line. **X<5** means x can be **any value less than 5**

**Reversal property of inequality**

### ** If a < b then b > a**