176 Chapter 2 Linear Equations and Inequalities in One Variable �������������������������������������� ���������������������������������������������������������������� The interval must be written in order from smallest to The interval is -2, -∞). ANSWERS TO STUDENT CHECKS largest or from left to right. Since the graph continues indefinitely to the left, the interval begins at -∞ and ends at the right with -2. So, the interval is (-∞, -2. Graph Interval Notation Set-Builder Notation Student Check 1 a. Student Check 2 a. Student Check 3 a. –5 –4 –3 –2 –1 0 1 2 3 4 5 (-2, ∞) Exux>-2F Student Check 1 b. Student Check 2 b. Student Check 3 b. –6 –5 –4 –3 –2 –1 0 1 2 3 4 (-∞, -4.2) Exux≤-4.2F Student Check 1 c. Student Check 2 c. Student Check 3 c. –6 –5 –4 –3 –2 –1 0 1 2 3 4 a-∞, 5 3 b e x` x < 5 3 f Student Check 1 d. Student Check 2 d. Student Check 3 d. –5 –4 –3 –2 –1 0 1 2 3 4 5 -4, 2) Exu-4 ≤ x < 2F Student Check 4 a. –7 –6 –5 –4 –3 –2 –1 0 1 2 3 (-∞, -5) Eyuy<-5F b. –7 –6 –5 –4 –3 –2 –1 0 1 2 3 -2, ∞) Exux ≥ -2F c. –5 –4 –3 –2 –1 0 1 2 3 4 5 1, ∞) Eyuy > 1F d. –5 –4 –3 –2 –1 0 1 2 3 4 5 c 11 7 , ∞b e aP a ≥ 11 7 f e. –5 –4 –3 –2 –1 0 1 2 3 4 5 a-∞, - 1 2 b e yP 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 (-∞, ∞) Exux is a real numberF h. 0 1 2 3 4 5 6 7 8 9 10 c 5 3 , 3 d e x` 5 3 ≤ x ≤ 3 f 6b. Solve -6x + 2 > 8. �������������������������������������� ���������������������������������������������������������������� -6x + 2 > 8 -6x + 2 - 2 > 8 - 2 -6x > 6 -6x -6 > 6 -6 x>-1 The solution is (-1, ∞). The only error made was that the inequality symbol was not reversed when both sides were divided by a negative number. -6x + 2 > 8 -6x + 2 - 2 > 8 - 2 -6x > 6 -6x -6 < 6 -6 x < - 1 The solution is (-∞, -1).
hendricks_beginning_algebra_1e_ch1_3
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