Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Linear Inequalities and Absolute Value Chapter 3
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec Set Operations and Compound Inequalities
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Objectives 1.Find the intersection of two sets. 2.Solve compound inequalities with the word and. 3.Find the union of two sets. 4.Solve compound inequalities with the word or.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Find the Intersection of Two sets The intersection of two sets is defined using the word and. Intersection of Sets AB
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Find the Intersection of Two Sets –3 –
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Compound Inequalities A compound inequality is a statement made by combining two inequalities with the words and or or. Examples of Compound Inequalities
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities To solve compound inequalities with the word and, use the following steps. Step 1Solve each inequality individually. Step 2Since the inequalities are joined with and, the solution set of the compound inequality will include all numbers that satisfy both inequalities in Step 1 (the intersection of the solution sets).
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 1Solve each inequality individually.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2Because the inequalities are joined by the word and, the solution will include all numbers that satisfy both inequalities in Step 1. The graphs of the two inequalities are: –5–4–3–2– –5–4–3–2–
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2Find the intersection of the two graphs. –5–4–3–2– –5–4–3–2– –5–4–3–2–
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 1 Solve each inequality in the compound inequality individually.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2Because the inequalities are joined by the word and, the solution will include all numbers that satisfy both inequalities in Step 1. The graphs of the two inequalities are: 16–2– –2– –2– –2–
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2 1 6–2– –2– –2– –2– Find the intersection of the two graphs. 16–2– –2–
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 1 Solve each inequality in the compound inequality individually.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2Because the inequalities are joined by the word and, the solution will include all numbers that satisfy both inequalities in Step 1. The graphs of the two inequalities are: –5–4–3–2– –5–4–3–2–
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 2Find the intersection of the two graphs. –5–4–3–2– –5–4–3–2– –5–4–3–2– The intervals do not overlap.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Find the Union of Two sets The union of two sets is defined using the word or. Union of Sets AB
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Find the Union of Two Sets –3 –
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities To solve compound inequalities with the word or, use the following steps. Step 1Solve each inequality individually. Step 2Since the inequalities are joined with or, the solution set includes all numbers that satisfy either one of the two inequalities in Step 1 (the union of the solution sets).
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 1 Solve each inequality individually.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities The graphs of these two inequalities are: –10–8–6–4– –10–8–6–4– Solve the compound inequality:
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Step 2Because the inequalities are joined by the word or, find the union of the two solution sets. –10–8–6–4– It would be wrong to write since it implies that.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Solve the compound inequality: Step 1 Solve each inequality in the compound inequality individually.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities The graphs of these two inequalities are: –5–4–3–2– –5–4–3–2– Solve the compound inequality:
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec Set Operations and Compound Inequalities Solving Compound Inequalities Step 2Because the inequalities are joined by the word or, find the union of the two solution sets. –10–8–6–4– By taking the union, we obtain every real number as a solution set.