Inequalities Denoting Inequalities Properties Solving Inequalities

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

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

Examples of Notation 4

Properties of Inequalities 5

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

An Example of Solving an Inequality 7

Another Example of Solving an Inequality 8

Yet Another Example of Solving an Inequality 9

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