a 1.4 Sets, Inequalities, and Interval Notation Determine whether a given number is a solution of an inequality. 1.4 Sets, Inequalities, and Interval Notation An inequality is a sentence containing Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

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

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

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

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

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

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

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

Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. The Addition Principle for Inequalities c Solve an inequality using the addition principle and the multiplication principle and then graph the inequality. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 9

Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. The Multiplication Principle for Inequalities For any real numbers a and b, and any positive number c: c Solve an inequality using the addition principle and the multiplication principle and then graph the inequality. For any real numbers a and b, and any negative number c: Similar statements hold for Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 10

c Solve an inequality using the addition principle and the multiplication principle and then graph the inequality. 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. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.

Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Translating “At Least” and “At Most” d Solve applied problems by translating to inequalities. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 12

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

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