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Inequalities

Inequalities. 1. Denoting Inequalities. 2. Properties. 3. Solving Inequalities. Definition. An inequality is a statement that two quantities or expressions are not equal. Denoting Inequalities. Notation Endpoints are the extreme limits of the inequality Closed Interval

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Inequalities

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  1. Inequalities 1 Denoting Inequalities 2 Properties 3 Solving Inequalities www.themegallery.com

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

  4. Examples of Notation

  5. Properties of Inequalities

  6. Solving Inequalities • Solve as you would an equation… With three new rules • Reverse the signs (i.e. < to >, 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) www.themegallery.com

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

  8. Another Example of Solving an Inequality

  9. Yet Another Example of Solving an Inequality

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

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