1. Inequalities www.themegallery.com 33 22 11 Denoting Inequalities Properties Solving Inequalities

2. Definition  An inequality is a statement that two quantities or expressions are not equal 2 www.themegallery.com

3. Denoting Inequalities  Notation  Endpoints are the extreme limits of the inequality  Closed Interval Denoted by [ ] Includes the endpoint(s) Associated with ≥ and ≤  Open Interval Denoted by ( ) Includes all values up to, but not including the endpoint(s) Associated with > and < 3 www.themegallery.com

4. Examples of Notation 4

5. Properties of Inequalities 5

6. Solving Inequalities  Solve as you would an equation… With three new rules  Reverse the signs (i.e., etc.) when: Dividing by a negative number Multiplying by a negative number Swapping positions of the variable and final answer Variable needs to be on the left in the event of a single inequality symbol Variable needs to be in the middle in the event of two inequality symbols (continued inequality) 6 www.themegallery.com

7. An Example of Solving an Inequality 7 www.themegallery.com

8. Another Example of Solving an Inequality 8

9. Yet Another Example of Solving an Inequality 9

10. Practice Problems  Page 119 Problems 3-46 Do not sketch graphs 10