Math Chaper 6 Review Answer Key

Chapter 6 Test Review Algebra 1 CP Name: Key Hour: Translate the verbal phrase into an inequality. Then graph the inequality. 1. All real numbers that are less than 5. x < 5 [Image of a number line with an open circle at 5 and an arrow pointing to the left] 2. All real numbers that are greater than or equal to -1. x ≥ -1 [Image of a number line with a closed circle at -1 and an arrow pointing to the right] 3. All real numbers that are greater than -2 and less than or equal to 7. -2 < x ≤ 7 [Image of a number line with an open circle at -2, a closed circle at 7, and a line segment connecting them] 4. All real numbers that are greater than 8 or less than -4. x > 8 or x < -4 [Image of a number line with an open circle at -4, an open circle at 8, and arrows pointing away from each circle] Solve the inequality, if possible. 5. x + 9 > 5 x > -4 6. 2 > 5 - y -3 > -y 3 < y y > 3 7. -0.8 ≤ 2 + 0.7y -2.8 ≤ 0.7y -4 ≤ y y ≥ -4 8. n/6 < -1 n < -6 9. r/-3 ≤ 4 r ≥ -12 10. -4s < 6s + 1 -10s < 1 s > -1/10 11. t - 7 ≤ 13 t ≤ 20 12. 4t - 7 ≤ 13 4t ≤ 20 t ≤ 5 13. -8 > 5 - v -13 > -v 13 < v v > 13 14. 3(5w + 4) < 12w - 11 15w + 12 < 12w - 11 3w < -23 w < -23/3 15. 4p - 3 ≥ 2(2p + 1) 4p - 3 ≥ 4p + 2 -3 ≥ 2 No solution 16. -9q - 12 ≥ 3(3q - 4) -9q - 12 ≥ 9q - 12 -18q ≥ 0 q ≤ 0 17. -2 ≤ 4 - 3a ≤ 13 -6 ≤ -3a ≤ 9 2 ≥ a ≥ -3 -3 ≤ a ≤ 2 18. -7 < 2c - 1 < 10 1/2 -6 < 2c < 11 1/2 -3 < c < 23/4 19. -5 ≤ 2 - h or 6h + 5 ≥ 71 -7 ≤ -h or 6h ≥ 66 7 ≥ h or h ≥ 11 Solve the absolute value equation or inequality, if possible. 21. |x-3| = -1/3 No Solution 22. 4|2z+5| + 9 = 5 4|2z+5| = -4 |2z+5| = -1 No Solution 23. |m| ≥ 8 m ≥ 8 or m ≤ -8 24. 6|k+1| ≥ 2 6|k+1| ≥ 2 |k+1| ≥ 1/3 k+1 ≥ 1/3 or -(k+1) ≥ 1/3 k ≥ -2/3 or k ≤ -4/3 25. |3g-2| < 5 -5 < 3g-2 < 5 -3 < 3g < 7 -1 < g < 7/3 26. 6|x+5| ≤ 14 |x+5| ≤ 7/3 -7/3 ≤ x+5 ≤ 7/3 -34/3 ≤ x ≤ -8/3 27. |2j-9| ≥ 12 2j-9 ≥ 12 or -(2j-9) ≥ 12 2j ≥ 21 or 2j ≤ -3 j ≥ 21/2 or j ≤ -3/2 28. |d+8| - 7 > 13 |d+8| > 20 d+8 > 20 or -(d+8) > 20 d > 12 or d < -28 29. Your friend is starting a small business baking and decorating cakes and wants to make a profit of at least $250 for the first month. The expenses for the first month are $155. What are the possible revenues that your friend can earn in order to meet the profit   goal? r = revenue Revenue - expenses = profit r - 155 ≥ 250 r ≥ 405 30. In men's gymnastics, an athlete competes in 6 events. Suppose that an athlete's average score per event is at most 9.7 points. Write and solve an inequality to find the possible total scores for the athlete.   # events * avg. score ≤ total possible pts 6 * 9.7 ≤ total possible pts 58.2 ≤ total possible pts 31. You can order discount movie tickets from a website for $7 each. You must also pay a shipping fee of $4. You want to spend no more than $40 on movie tickets.   Find the possible numbers of movie tickets that you can order.   t = # tickets 7t + 4 ≤ 40 7t ≤ 36 t ≤ 5.14 ≈ 5 tickets 32-33. Solve the following inequalities. Graph your solution. 32. |2x+1| ≥ 5 2x+1 ≥ 5 or -(2x+1) ≥ 5 2x ≥ 4 or -2x ≥ 6 x ≥ 2 or x ≤ -3 [Image of a number line with closed circles at -3 and 2, and arrows pointing outward from both] 33. 2|3f-7| + 5 ≤ 11 2|3f-7| ≤ 6 |3f-7| ≤ 3 -3 ≤ 3f-7 ≤ 3 4 ≤ 3f ≤ 10 4/3 ≤ f ≤ 10/3 [Image of a number line with closed circles at 4/3 and 10/3, and a line segment connecting them] 34. A manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inch with an absolute error of at most 0.0003 inch. Find the possible widths of bicycle chains that the manufacturer will accept. |x - 0.3| ≤ 0.0003 x - 0.3 ≤ 0.0003 or -(x - 0.3) ≤ 0.0003 x ≤ 0.3003 or x ≥ 0.2997 0.2997 ≤ x ≤ 0.3003 Tell whether the ordered pair is a solution of the inequality. 35. 2x - y > 4; (-6, -15) 2(-6) - (-15) > 4 -12 + 15 > 4 3 > 4 No! 36. 4x - 3y ≥ -5; (6, 8) 4(6) - 3(8) ≥ -5 24 - 24 ≥ -5 0 ≥ -5 Yes! Graph the following inequalities. 37. y ≤ x + 4 [Image of a graph with a solid line y = x + 4 and the shaded region below the line] 38. 6y + 3x ≥ -18 6y ≥ -3x - 18 y ≥ -1/2x - 3 [Image of a graph with a solid line y = -1/2x - 3 and the shaded region above the line] 39. y ≥ -6 [Image of a graph with a horizontal solid line at y = -6 and the shaded region above the line] Write an inequality for the graph shown. 40. [Image of a graph with a line passing through (0, 4) and (4, 0)] m = -1 b = 4 y ≥ -x + 4 41. [Image of a graph with a line passing through (0, 3) and (4, 0)] m = -3/4 b = 3 y ≤ -3/4x + 3 42. [Image of a graph with a line passing through (-1, -3) and (0, -1)] m = -2 b = -1 y ≤ -2x - 1