96 Chapter 2 Linear Equations and Inequalities in One Variable Graph Interval Notation Set-Builder Notation Student Check 1 a. –6 –5 –4 –3 –2 –1 0 1 2 3 4 (-1, ∞) 5xux>-16 b. –2 –1 0 1 2 3 4 5 6 7 8 3, ∞) 5xux ≥ 36 c. –6 –5 –4 –3 –2 –1 0 1 2 3 4 (-∞, -1) 5xux<-16 d. –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 -∞, -3 5xux≤-36 e. –1 0 1 2 3 4 5 6 7 8 9 (2, 7) 5xu2 < x < 76 Student Check 2 a. –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 (-∞, -5) 5yuy<-56 b. –7 –6 –5 –4 –3 –2 –1 0 1 2 3 -2, ∞) 5xux≥-26 c. –4 –3 –2 –1 0 1 2 3 4 5 6 (1, ∞) 5yuy > 16 d. 11 7 –4 –3 –2 –1 0 1 2 3 4 5 6 c 11 7 , ∞b e a` a ≥ 11 7 f e. 1 2 – –5 –4 –3 –2 –1 0 1 2 3 4 5 a-∞, - 1 2 b e y` y<- 1 2 f f. –5 –4 –3 –2 –1 0 1 2 3 4 5 g. –5 –4 –3 –2 –1 0 1 2 3 4 5 (-∞, ∞) 5xux is a real number6 Student Check 3 a. Bryan needs at least 54 on his fourth test to have at least a 70 test average. b. Tomekia needs at least 74 on the final exam to have a final average of at least 80. c. Jared and Angela can invite at most 125 people to have a cost of no more than $4000. SUMMARY OF KEY CONCEPTS 1. The graph of the solution set of an inequality is a picture of all real numbers that make the inequality a true statement. A parenthesis (used with < or >) on a number indicates the number is not included in the solution set. A bracket (used with ≤ or ≥) on a number indicates the number is included in the solution set. We can use interval notation or set-builder notation to express the solution set. a. Interval notation begins with the left bound of the solution set and ends with the right bound of the solution set. When the numbers in a set continue indefinitely to the right, the right bound is represented by ∞. When the numbers in a set continue indefinitely to the left, the left bound is represented by -∞. A parenthesis is always used with ∞ or -∞. b. Set-builder notation is written using 5 6. We write 5variableufinal inequality6. Example: 5yuy < 56. 2. Inequalities are solved using the addition and multiplication properties of inequalities. The most important thing to remember is that when we multiply or divide by a negative number, we must also reverse the inequality symbol. ANSWERS TO STUDENT CHECKS
hendricks_intermediate_algebra_1e_ch1_3
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