Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: ______________________ Class: _________________ Date: _________ Algebra 1 Solving Inequalities Review What inequality represents the verbal expression? 1. all real numbers greater than or equal to 67 2. all real numbers less than 69 3. 8 less than a number n is less than 11 a. 11 – 8 < n b. n – 8 < 11 c. d. 8 – n < 11 11 < 8 – n Which number is a solution of the inequality? 4. m > a. 7 12 1 5. 6 ≥ 6k a. 8 b. –1 c. –9 d. –5 b. 18 c. 2 d. 1 What is the graph of the inequality? 6. d < 2 7. x ≥ –3 What inequality represents the graph? 8. 9. What inequality describes the situation? 10. Let n = the number. A number exceeds 45. What are the solutions of the inequality? Graph the solutions. 11. x − 3 ≤ − 12 12. y − 6 ≤ 2 13. r – 5 > 4 1 ID: A Name: ______________________ ID: A What are the solutions of the inequality? Graph the solutions. 14. x + 7 ≤ − 8 15. b + 8 ≤ 4 16. p + 4 > 1 17. Suppose you had d dollars in your bank account. You spent $12 but have at least $51 left. How much money did you have initially? Write and solve an inequality that represents this situation. 18. Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated the first week and 89 more the second week. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal? What are the solutions of the inequality? Graph the solutions. 19. x >9 9 20. x ≥ −2 5 What are the solutions of the inequality? Graph and check the solutions. 21. − x ≤2 4 1 22. − x ≤ 5 8 23. The French Club is sponsoring a bake sale. If their goal is to raise at least $140, how many pastries must they sell at $3.50 each in order to meet that goal? Write and solve an inequality. What are the solutions of the inequality? Graph the solutions. 24. −4x ≥ −12 25. –2m < –14 2 Name: ______________________ ID: A What are the solutions of the inequality? Check the solutions. 26. – 2 9 x–9< 5 10 27. 4x + 6 < –6 What are the solutions of the inequality? 28. 2(b – 8) > 12 29. q + 12 – 2(q – 22) > 0 What are the solutions of the inequality? 30. 12 + 10w ≥ 8(w + 12) 31. 12x – 3x + 11 > 4x – (17 – 9x) 32. 8n − 14 ≤ 13n + 6 What are the solutions of the inequality? 33. −5 ( 2x + 2 ) ≥ −10x − 17 a. x ≥ 7 b. x ≤ 19 c. d. all real numbers no solution 34. 10x − 10 − 7x ≥ 3x − 2 a. x ≥ −8 b. x ≤ 8 c. d. all real numbers no solution How do you write the set in roster form? In set builder notation? 35. D is the set of whole numbers less than 3. a. D = {0,1,2,3,4,5}; D = {x is a whole number, x < 3} b. D = {0,1}; D = {x | x < 3} c. D = {0,1,2}; D = {x | x is a whole number, x < 3} d. D = {0,1,2,3,4,5,6,7}; D = {x < 3} 36. G is the set of odd natural numbers that are less than or equal to 1. 37. H is the set of even integers less than 6 but greater than or equal to 0. 3 Name: ______________________ ID: A In set builder notation, how do you write the solutions of the inequality? 38. 3x + 10 ≥ 4 ÔÏ Ô¸ a. ÌÔ x | x ≥ −2 ˝Ô Ó ˛ ÔÏ Ô¸ b. ÌÔ x | x ≤ 2 ˝Ô Ó ˛ 39. −2 − x ≥ −1 ÏÔ ¸Ô a. ÔÌ x | x ≤ 1 Ô˝ Ó ˛ ÏÔ ¸Ô b. ÔÌ x | x ≥ 1 Ô˝ Ó ˛ c. d. c. d. ÔÏ Ô¸ ÌÔ x | x ≤ −2 ˝Ô Ó ˛ ÔÏ Ô¸ ÌÔ x | x ≥ 2 ˝Ô Ó ˛ ÏÔ ¸Ô ÔÌÓ x | x ≥ −1 Ô˝˛ ÏÔ ¸Ô ÔÌÓ x | x ≤ −1 Ô˝˛ What are all the subsets of the set? 40. {–1, 9} a. ∅, {−1}, {9} b. {−1}, {9}, {−1, 9} c. d. ∅, {−1}, {9}, {−1, 9} {−1}, {9} 41. Suppose U = {–10, –6, –2, 0, 3, 5} is the universal set and T is the set {–10, –6, 0}. What is the complement of set T? a. {–2, 3, 5} c. {–6, –2, 0, 3, 5} b. {–10, –6, 0} d. {0, 3, 5} 42. Suppose U = {–4, 3, 4, 5, 9, 10} is the universal set and T is the set {–4, 3, 5}. What is the complement of set T? a. {–4, 3, 5} c. {4, 9, 10} b. {5, 9, 10} d. {3, 4, 5, 9, 10} What compound inequality represents the phrase? Graph the solutions. 43. all real numbers that are greater than –8 and less than 8 44. all real numbers w that are less than –7 or greater than 14 45. all real numbers at least –5 and at most 9 46. all real numbers at most –8.5 or at least 6.5 What are the solutions of the compound inequality? Graph the solutions. 47. −2 ≤ 2x − 4 < 8 48. –2 < 4x – 10 < 6 4 Name: ______________________ ID: A What are the solutions of the compound inequality? Graph the solutions. 49. 2x – 2 < –12 or 2x + 3 > 7 50. 2x − 1 + 3 ≤ −4 3 or 8x − 2 −1≥ 6 2 51. What is the graph of (–8, 2]? a. b. c. d. 52. How do you write x ≥ −6 and x < −3 in interval notation? a. b. [–6, –3] (–6, –3) c. d. [–6, –3) (–6, –3] 53. What is the graph of (−∞, −8) or (6, ∞)? a. b. c. d. 54. How do you write (−∞, 8) or (10, ∞) as an inequality? a. b. x < 8 or x > 10 x < 10 or x > 8 c. d. x < 8 and x > 10 x < 10 and x > 8 5 Name: ______________________ ID: A Let X = {x | x is a whole number less than 15}, Y = { x | x is a multiple of 3}, Z = {x | x is a real number greater than or equal to 5.5}. 55. What is X ∩ Y? 56. What is X ∩ Z? 57. A doctor is examining 3 patients. Which symptoms do all three patients have in common? 58. Of 410 consumers polled, some purchase music on CDs, some only download music, and some do both. If 290 people polled purchase CDs and 220 purchase CDs and download music, how many people download music? 59. Of 480 consumers polled, some purchase ice cream, some purchase frozen yogurt, and some purchase both. If 260 people polled purchase ice cream and 200 purchase both ice cream and frozen yogurt, how many people purchase frozen yogurt? CUMULATIVE REVIEW SEÇTION 2 60. 5 ( 14 − 2 ) ÷ 2 ÍÈÍ 2 Ê 2 ˙˘˙ 2ˆ 61. 13 ÍÍÍ 6 ÷ ÁÁÁÁ 5 − 4 ˜˜˜˜ + 9 ˙˙˙ ÍÎ ˙˚ Ë 62. Evaluate u + xy, for u = 18, x = 10, and y = 8. 6 Name: ______________________ 63. Evaluate ID: A u 2 + xy , for u = 20, x = 4, y = 7, and z = 10. z 64. To which subsets of the real numbers does the number 22 belong? 65. To which subsets of the real numbers does the number 42 belong? What is each difference? 66. 9 1 − 4 7 What is each product? 67. 5 10 • 10 3 What is the simplified form of each expression? 68. 1 (21m + 27) 3 What is the solution of the equation? 69. 3(y – 5) + 2 = 5 70. 2.4x + 2.6 = 17 What is the solution of the equation? 71. 6x – 3 = 5x – 5 72. –4x – 9 = –5 – 6x What is the solution of the equation? 73. 5 ( 10x − 10 ) = −5 ( −4x + 4 ) What is the solution of each equation? 74. 2(h − 8) − h = h − 16 a. 8 b. −8 c. d. infinitely many solutions no solution 7 Name: ______________________ 75. 3 + 6z = 13 + 6z 5 a. − 6 2 b. 2 3 ID: A c. infinitely many solutions d. no solution What is the given amount converted to the given units? 76. 195 s; minutes 77. A car is driving at a speed of 45 mi/h. What is the speed of the car in feet per minute? What is the solution of the proportion? 78. h 19 = −8 −2 a. 76 b. –152 c. d. –38 16 8 ID: A Algebra 1 Solving Inequalities Review Answer Section 1. 2. 3. 4. 5. x ≥ 67 x < 69 B A D 6. 7. 8. x > –8 1 2 10. n > 45 11. x ≤ − 9 9. m ≥ − 12. y ≤ 8 13. r > 9 14. x ≤ − 15 15. b ≤ − 4 16. p > –3 17. d − 12 ≥ 51; d ≥ 63 18. 135 + 89 + c ≥ 325; c ≥ 101 19. x > 81 20. x ≥ − 10 1 ID: A 21. x ≥ − 8 22. x ≥ −40 23. 3.50p ≥ 140; p ≥ 40 24. x ≤ 3 25. m > 7 26. x > −24 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 3 4 x < –3 b > 14 q < 56 w ≥ 42 x<7 n ≥ –4 C D C G = {1}; G = {x | x is an odd natural number, x ≤ 1} ÔÏ Ô¸ H = ÌÔ 0, 2, 4 ˝Ô ; H = {x | x is an even integer, x < 6, x ≥ 0} Ó ˛ A D C A C –8 < x < 8 44. w < –7 or w > 14 45. −5 ≤ x ≤ 9 46. b ≤ − 8.5 or b ≥ 6.5 2 ID: A 47. 1 ≤ x < 6 48. 2 < x < 4 49. x < –5 or x > 2 50. x ≤ − 10 or x ≥ 2 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. C C C A {0, 3, 6, 9, 12} {6, 7, 8, 9, 10, 11, 12, 13, 14} {fever, joint pain, tiredness} 340 420 360 169 98 198 integers, rational numbers irrational numbers 59 28 5 3 7m + 9 6 6 –2 2 1 C D 3.25 min 3,960 ft/min A 3