1. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. An inequality is a sentence containing 1.4 Sets, Inequalities, and Interval Notation

2. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Determine whether the given number is a solution of the inequality.

3. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. We substitute –3 for x and get or a true sentence. Therefore, –3 is a solution. Determine whether the given number is a solution of the inequality.

4. Graph on the number line. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. The graph of an inequality is a drawing that represents its solutions.

5. Write interval notation for the solution set or the graph of an inequality. Slide 5 Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

6. Write interval notation for the solution set or the graph of an inequality. Slide 6 Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

7. Write interval notation for the solution set or the graph of an inequality. Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

8. Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

9. The Addition Principle for Inequalities Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

10. The Multiplication Principle for Inequalities Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. For any real numbers a and b, and any positive number c: For any real numbers a and b, and any negative number c: Similar statements hold for

11. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. The multiplication principle tells us that when we multiply or divide on both sides of an inequality by a negative number, we must reverse the inequality symbol to obtain an equivalent inequality.

12. Translating “At Least” and “At Most” Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

13. Solve applied problems by translating to inequalities. Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

14. Solve applied problems by translating to inequalities. Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.