112 Chapter 2 Linear Equations and Inequalities in One Variable e. c- 11 7 , 2 d 11 7 – –5 –4 –3 –2 –1 0 1 2 3 4 5 Student Check 4 a. (-∞, 5) ∪ (5, ∞) 0 1 2 3 4 5 6 7 8 9 10 b. a-∞, - 5 6 b ∪ c 8 9 , ∞b – 8 5 6 9 –5 –4 –3 –2 –1 0 1 2 3 4 5 c. (-∞, ∞) –5 –4 –3 –2 –1 0 1 2 3 4 5 Student Check 5 a. Bryan should weigh between 136 and 184 lb. b. Ameena must score between 85 and 100 on her final to make a 70–79 in chemistry. SUMMARY OF KEY CONCEPTS 1. Elements that two sets have in common form the intersection of the two sets. 2. The elements that are in either set form the union of the two sets. 3. To solve a compound inequality involving “and” means to find the intersection of the solution sets of each inequality. 4. To solve a compound inequality involving “or” means to find the union of the solution sets of each inequality. GRAPHING CALCULATOR SKILLS We can use the graphing calculator to graph the solution set of a compound inequality. It is best to solve the inequality by hand and then use the calculator to confirm the solution. Example 1: Solve x + 6<-1 or 2x>-4. Solution: Enter the compound inequality into Y1. Insert parentheses around each inequality. Use the Test menu (2nd Math) to access the inequality symbols and the coordinating conjunction “or” (2nd Math, Logic). Then graph the solution. The interval that contains the solutions will be highlighted above the x-axis. Y= ( X,T,u,n + 6 2nd ATH 5 (–) ) 2nd ATH 2 ( 2 X,T,u,n 2nd ATH 3 (–) 4 ) –7 –2 GRAPH So, the solution set is (-∞, -7) ∪ (-2, ∞). Example 2: x + 5 ≥ 8 and -2x≥-10. Solution: Enter the compound inequality into Y1. Use the Test menu (2nd Math) to access the inequality symbols and the coordinating conjunction “and” (2nd Math, Logic). Then graph the solution. The interval that contains the solutions will be highlighted above the x-axis. Y= ( X,T,u,n + 5 2nd ATH 4 8 ) 2nd ATH ( (–) 2 X,T,u,n 2nd ATH 4 (–) ) 3 5 GRAPH So, the solution set is 3, 5.
hendricks_intermediate_algebra_1e_ch1_3
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