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Name ________________________________ Math Period ______ Chapter 11 Equations & Inequalities Write a P for positive or N for negative above each term then simplify the following:

1. 2a + 4a + 8a

2. 5x + 6x + 9x

3. 3n + 9n + 11n

4. 5y + 6y + 14y

5. 6p + 9p – 5p

6. 2w + w + w + 4w

7. 8x + 17x + x

8. 4g + 9g + 8q

9. 3c + 9c + c + 7c

10. 8w + 8f + 8w

11. 9a + 8m + 3m

12. 5w + 15v + 8w + 6

13. 4j + 9h + 9j + 7j

14. 2x + x + 3x + 5

15. 9f + 5y + 3f + 4y

16. 4x + 7y + x + y

17. 18x + 14 + x + 17x + 6

18. 5c + 2c + 8c + c

19. 9w – 4w

20. 4x – 3x

21. 2c + –6c

22. 5x – 8x

23. 3x – –12x

24. 3w – 8w

25. –6p – 2p

26. 3k – –9k

27. 15x – 19x

28. –x – x

29. x – – 2x

30. c + 3c

31. 5x – 2x

32. 3x – – 2x

33. 4w – 9w

34. – 5p – p

35. 6k – – 5k

36. x – 9x

37. – 8x – x

38. 5 + x – 3

39. 3 – – j – 10

40. g – 5 – 3g

41. 12 – 3q – 9

42. 5 – x – 6

43. 3 + x + 6

44. 7 – –k – 4

45. 8g – 2 – 2g

46. 4q – 15

47. 7 – 5x – –6x

48. 8 + 9p – 6 – 2p

49. 4x + 7 – 4x – 7

50. 3w – 6 + 3w – 8

51. – x + 7 – 4x – 5

52. 9 + 6x + 5x – l

53. 9 – 4 + 17k – 3

54. 13r + 5s – 6r – 2s

55. 23m + 4n – –16m

56. 5y – 9 – 3y + 11

57. 5q – 2w + 9w – 8g

58. 24b – 4b – 6b – –9b

59. 6h – v + 27v + 5h

60. 13f – 7g + 18f + 4f

61. 2k – 7 + 11k – –14k

62. 7m –- 2m – 8m – m

63. –15 + 12x + 11 – 13x

64. 6c + 2h – –9c + 3h

65. 12 + 5v + 4v – 8 – 9v

66. 26 + 36b + 4b + 30b

67. 2x + 6 – x – 5

68. w – 5 – 3w – – 7

69. – x – 1 – 2x – 3

70. – 3r + 4s – 7r – s

71. 12m – n – 23m – 4n

72. 2y – 7 – 4y + 16

73. 9g – 8w + 2w – 4g

74. 14b – 3b – b – – 5b

75. 3h – v + 9v + 17v + 9h

76. 4f – 5q + 13f – 6f

77. 9k + 5 + 13k – – 18k

78. – 6m – 4m – 8m – m

79. –16 + 14x + 17 – 14x

80. 5c + 3h – – 5c + 4h

81. 4x – 6x – 7x – 9x

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Distributive Property Simplify the following using the Distributive Property: 1. 2 ( x + 6 ) 2. 3 ( x + 9 ) 3. 5 ( x – 8 ) 4. 6 ( 8 – x ) 5. 3 ( 2 – g ) 6. 8 ( 4 + 2 x ) 7. 9 ( 5 + 8x ) 8. 5 ( 2 + 3x ) 9. 8 ( 9 – 3y ) 10. 4 ( 8 – 6y ) 11. –3 ( x + 5 ) 12. –7 ( 3 + x ) 13. –5 ( 3x + 7 ) 14. –4 ( 8x + 7 ) 15. –8 ( 5 + 3x ) 16. –7 ( 4 + 8x ) 17. –2 ( 8 + 10y )

18. –3 ( 2 – 3x ) 19. –7 ( 5 – 9x ) 20. –8 ( 7x – 3 ) 21. –5 ( 3 – 4x ) 22. –4 ( 10 – 2x ) 23. –3 ( 7 – 4x ) 24. –9 ( 3x – 5 ) 25. –5 ( 8x – 6 ) 26. –5 (–3x – 7 ) 27. –2 (–x – 5 ) 28. –3 (–9 – 11x ) 29. –11 (–2 – 5x ) 30. –5 ( 3x + 2y ) 31. –7 ( 5x – 6y ) 32. –5 ( 7x – 3y ) 33. –6 ( 2x – 5y ) 34. –5 (–8x – 12y )

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Distributive Property & SimplifySimplify the following. Show all steps. 1. 4 ( 6 + 7x )

2. 9 ( 2x + 7 ) 3. ( 4x – 3 ) 8 4. ( 3x + 4 ) 2 5. 6 ( 2x + 9y) 6. 5 ( 3x + 15 ) 7. 3 ( 2 + 3x ) 8. 4 ( 8x – 7 ) 9. ( 6x – 3 ) 5

10. ( 7x – 3 ) 2 11. 2 ( 6x + 8y ) 12. 4 ( 8x + 5 ) 13. 4 ( 2x + 5 ) + 11 14. 2 ( 4 + 8x ) + 12 15. 5 ( x + 13 ) + x 16. 4 ( 5x + 12 ) + 6x 17. 2 ( x – 11 ) + 9x 18. 11( 4x + 3y ) – 6y 19. 8y + 4 ( 3y – 5 ) 20. 2m – 7( 8w + 9m ) 21. 6x – 6 ( 6x – 7 ) 22. 2w + 7 ( 7w – 9 ) 23. 9 – 4 ( 2n + 3 ) 24. 6 – 5 ( 3 – 9c )

25. 3 ( 2x + 8 ) – 6 26. 7 ( 4 + 7x ) – 5 27. 3 ( 2x – 11 ) – 10x 28. 3 ( 5 + x ) – 6 29. 5 ( 6x + 8 ) – 3x 30. 9 ( 3x – 2y ) + 9y 31. 7y – 4 ( 2y – 9 ) 32. 3m – 8 ( 7w + 6m ) 33. 4x + 8 ( 3x – 4 ) 34. 6w – 5 ( 9w + 6 ) 35. 7 – 3 ( 2 + 3n ) 36. 1 + 5 ( 7n – 8 ) 37. 3 – 8 ( 11x – 4 } 38. 16 – 5 ( 4 – 8x ) 39. 6 ( 4z + 8 ) + ( 11z + 4 ) 40. 2 ( 6 + 5x ) + 3 ( 4 + 8x ) 41. – 3 ( 5 – 3w) – ( 5w + 4 ) 42. 7 ( 2c + 8 ) – ( 9 – 5c ) 43. – 6 ( 3y – 3p ) + 2 ( 5p + 4y ) 44. 9 ( 3x + 7 ) + ( 5x – 4 ) 45. – 11 ( 8 – 3h ) – 3 ( h – 2 ) 46. 9 ( 5 – 8d ) + 7 ( d + 9 ) 47. 8 ( k + m ) – ( k + m ) 48. 12 + 5 ( g – 6 ) + 8 ( 5 – g )

SOLVE the following equations showing all the work.

1. a – 11 = 15 2. b – 8 = 17 3. y + 7 = 29 4. x + 18 = 31 5. – 76 + m = 92 6. – 49 + n = 63 7. c – 30 = – 19 8. d – 24 = – 15 9. p + 18 = – 32 10. s + 90 = – 55 11. 24 + t = 0 12. 0 = z – 14 13. v – 37 = – 54 14. w – 94 = – 110 15. – 7 + k = – 17 16. – 18 + h = – 38 17. 45 = x + 16 18. 39 = y + 12 19. – 19 – a = – 23 20. b – 32 = – 82 21. 1 – x = 4 22. 16 = 3 – a 23. 18 = 5 – g 24. 3 – h = – 26 25. 25 = 18 – k 26. 4 = – p – 6 27. 45 – m = 15 28. 34 – r = 34 29. 52 = 81 – z

30. 61 = – y – 4 31. 36x = 72 32. 10y = – 10 33. 3c = – 21 34. – 8a = 32 35. 12 4b= 36. 13 7t = 37. − =1

10 5r 38. − =1

9 9s 39. 0 = – 4 k 40. – 7 = – 7p 41. c4 1= − 42. d2 2= 43. – 11f = – 88 44. – 27p = – 81 45. 4 3= − u 46. − =1 13

n 47. 5x – 1 = 26 48. 4y – 2 = 14 49. 2z + 4 = 8 50. 6 + 2a = 10 51. 9z – 5 = 4 52. 4y – 7 = 21 53. 6 = – 4x – 2 54. 4 – 3y = 13

55. – 4 = – 8 – 2z 56. – 7 = 3 + 5a 57. – 6x + 25 = – 11 58. 18 = 2c + 10 59. 17 – 3y = – 10 60. 8n – 14 = – 22 61. – x + 3 = – 4 62. 5 – m = 12 63. – 6 – z = – 2 64. – 4 = 6 – 2x

65. x 9 135+ =

66. x7 93

− = +

67. y5 43

+ = −

68. 1 x 7 23

− =

69. 36 y 95

− =

70. 317 10 z4

= − +

71. 32 = 7x + 8 – 5x 72. 6y + 8 – 5y = – 11 73. – 3 = 8z + 8 – 9z 74. 5 = 5x – 7x + 25 75. 3y + 7 – 5y = – 9 76. – 7 = 3p – 9 – 7p

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Solve the following equations. Show all work for each. 77. 9y – 18 = 3y

78. 7c – 9 = 8c

79. 8n – 12 = 5n

80. – 11m = 14 – 9m

81. – 6x = 10 – 4x

82. – 4z = 35 – 9z

83. 8p = – 5p + 65

84. – 84 + 15r = 3r

85. 11c + 36 = 8c

86. 7z – 9 = 3z + 19

87. 6 + 10t = 8t + 12

88. 3x + 7 = 16 + 6x

89. 18 + 3y = 5y – 4

90. 11a + 8 = – 2 + 9a

91. 9x – 5 = 6x + 13

92. 5 – x = x + 9

93. 14 + 3n = n – 14

94. 7 – x = 5 + 3x

95. 4y + 2 = 2y + 4 + 3y

96. 8c – 12 = 15c – 4c

97. 5x – 3 = 7x + 7 + 3x

98. y + 11 = – 2y + 6 99. – 2y + 3 – y = 11 + y 100. 16 – x = 4x + 8 + 3x 101. 2 ( y + 7 ) = 16 102. 3 ( x – 2 ) = 18

103. – 5 ( a + 2 ) = 30

104. x + 9 = 2 ( x – 3 )

105. 2 ( y + 3 ) = 12 – y

106. 25 – 5a = 3 ( 2a + 1 )

107. – 2 ( 3 – 2c ) = 10 – 4c

108. 23 = 12 – ( 6 + c )

109. 5 ( x – 1 ) = 2x + 4 ( x – 1 )

110. 13 – ( 2x – 5 ) = 2 ( x + 2 ) + 3x

111. – ( 3 – 2n ) + 7n = 3 ( n + 3 )

112. – ( y + 8 ) – 5 = 4 ( y + 2 ) – 6y

113. 3 ( c + 4 ) – 6c = 2 ( 4 – 2c )

114. 8y – 3 ( 4 – 2y ) = 6 ( y + 1 ) – 2

115. – 2 ( 3 – 4z ) + 7z = 12z – ( z + 2 )

116. – 3 ( 6 – 2x ) + 4x = – ( 2x – 6 ) 117. 7x – ( 9 – 4x ) = 3 ( x – 11 ) 118. 7r + 3 ( 7 – r ) = – ( r + 4 )

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Solve Word Problems 1 Use the verbal model format to set-up the following. SOLVE COMPLETELY. 1. Seven more than three times a number is eighteen. Find the number. 2. Jason has fourteen more than three times Evelyn’s amount. Together they have 130 marbles. How many marbles does each have? 3. Seven times the difference between eleven and twelve times a number is four. Find the number. 4. April has 9 computer games. This is seven less than twice the number of Sam’s games. How many does Sam have? 5. The quotient of nine times a number and fourteen is seven. Find the number. 6. One number is 28. This is nine more than three times a second number. Find the second number. 7. George has twelve books more than Jonathan. Together, they have 44 books. How many books does each have? 8. Julian has $65, which is $11 more than his friend Dylan. How many does Dylan have? 9. Six more than half a number is forty-two. Find the number. 10. Arthur has 23 books. This is twelve books less than Jonathan. How many books does Jonathan have? 11. The first number is seven times a second number. If the first number is 111, find the second number. 12. One number is sixteen more than five times a second number. Their sum is 58. Find the numbers. 13. Eleven is twice the sum of eight times a number and twelve. Find the number. 14. Greg has earned 4 more than twice the number of points as Matt. Together, they have earned 19 points. How many points has each earned? 15. Find the radius of a circle with the circumference of 13.65 feet. 16. John has 18 more papers to deliver than Sam. If John delivers 103 papers, how many does Sam deliver? 17. The measures of two of the angles of a triangle are 410 and 830, respectively. Find the measure of the

third angle. 18. Nineteen less than twelve times a number is 91. Find the number. 19. Find the height of a prism if its volume is 2295 ft3, its width is 15 ft and its length is 17 ft. 20. A triangle has a height of 38.2 m and an area of 324.7 m2. Find its base. 21. If it is 27˚C, what is the temperature in Fahrenheit? 22. If it is 6˚ F, what is the temperature in Celsius?

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Solve Word Problems 2 Use the verbal model format to set-up the following. SOLVE COMPLETELY. 1. Six less than five times a number is 86. Find the number. 2. Sue walked for 15 miles longer than Christine during the walk-a-thon. If Sue walked for 22 miles, how far

did Christine walk? 3. George has six more trophies than David. Together, they have 15 trophies. How many does each have? 4. Six times the difference between eight times a number and nine is five. Find the number. 5. Sally has $84.86 in her bank account. This is $17.34 more than a dress she wants to purchase. How

much does the dress cost? 6. Find the length of a rectangle if its perimeter is 29 yards and its width is 5 yards. 7. Andrew scored three goals more than David. Together, they scored five goals. How many did each

score? 8. Find the missing angle of a triangle if the measure of the first angle is 450 and the measure of the second

angle is 1010. 9. Nine less than seven times a number is the same as twelve times that number. Find that number. 10. The first of three numbers is six times the second. The third is nine less than the first. Their sum is 184.

Find the numbers. 11. A sofa costs $11 more than twice the chair. The table costs half as much as the chair. The total of the

sofa, table and chair is $1852. Find the cost of each. 12. The measure of one angle of a triangle is 850 and the measure of the second angle is 450. Find the

measure of the third angle. 13. One number is nine more than three times a second number. If their sum is 41, find both numbers. 14. Find the height of a rectangular prism if its length is 16 feet, its width is 21 feet and its surface area is 1412 square feet. 15. Find the side of a square when the area is 56 square yards. 16. A roller coaster at the bottom of a hill has a velocity of 25 m/sec. Two seconds later; it reaches the top of

the hill with a velocity of 35 m/sec. What is the acceleration of the roller coaster? 17. Lillian has 9 more dolls than Suzanne. Together, they have 41dolls. How many does each have? 18. Lillian has 9 more dolls than Suzanne. If Lillian has 25 dolls, how many does Suzanne have? 19. Find the side of a cube if its volume is 148.877 m3. 20. Find the height of a rectangular prism if its length is 11 feet, its width is 13 feet and its volume is 1144 cubic

feet. 21. The area of a triangle is 169 square feet. If its height is 13 feet, find the length of its base.

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Solve Word Problems 3 Use the verbal model format to set-up the following. SOLVE COMPLETELY. 1. A triangle has a perimeter of 57 feet. Find the missing side if the other two sides measure 12 feet and 18 feet, respectively. 2. The perimeter of a triangle is 84 m. One side measures 23 m and the other side measures 33 m. How long is the third side? 3. The perimeter of a rectangle is 64 cm. Find the length if the width is 13 cm. 4. The perimeter of a rectangle is 154 mi. Find the width if the length is 54 mi. 5. A car travels 135 miles in 6 hours. What is its average speed? 6. A man rides his bike at a rate of 8 miles per hour. How long will it take him to travel 72 miles? 7. John rows his boat 7 miles in 3 hours. What is his average rate? 8. Sue can run at an average speed of 2 km per hour. How long would it take her to run 9 kilometers? 9. Find the missing side of a trapezoid, if the perimeter is 54.2 m and the other sides measure 12.4 m, 18.1 m, and 7.2 m respectively. 10. The area of a rectangular dog run is 168 square feet. If the width is 8 feet, how long is the dog run? 11. The measures of two of the angles of a triangle are 240 and 480, respectively. Find the measure of the

third angle. 12. If it is 17˚C, what is the temperature in Fahrenheit? 13. If it is 56˚ F, what is the temperature in Celsius? 14. Find the side of a cube if its surface area measures 1176 square inches. 15. Find the height of a rectangular prism if its length is 16 feet, its width is 21 feet and its surface area is 1412 square feet. 16. What was the cost of the meal if an 18% tip was $10.99? 17. What was the original cost of a dress during a 25% off sale if the savings was $22.50? 18. Each towel cost $5.98. How many towels did Stephanie purchase for $89.70, if there was no sales tax? 19. Twelve of the same item cost $54 not including sales tax. How much did each item cost? 20. A company reimburses $49 plus forty-five cent for each mile a salesman drives. If the reimbursement

check was for $121, how many miles did the salesman drive? 21. A repair man charges a service fee of $60 plus $35 for each hour he works on the item. If the final bill was

$147.50, for how many hours did he work on the item?

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Forms of Inequalities A Complete the following table by writing the algebraic, graphic and descriptive forms of each.

ALGEBRAIC GRAPHIC DESCRIPTIVE

1 x > 40

2

x 3 4 5

3 all numbers that are greater than six

4

y – 8 – 7 – 6

5 y < – 4

6 all numbers that are less than 0

7 x ≥ 121

8

z 53 54 55

9 a > – 65

10 all numbers that are less than or equal to 166

11 8 ≤ b

12 – 17 < c

13 26 ≥ k

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INEQUALITIES Directions: Solve the following inequalities and write the answer in three forms (algebraically, graphically and by description):

1. x 5 7+ < 2. 4 x 12+ > − 3. x 8 17− − > − 4. 3 x 19− + > 5. 6 x 8+ ≤ − 6. x 10 6− ≥ − 7. 2x 7 4+ ≥ 8. 6 3x 15− ≤ 9. 4x 2 10− − ≥ 10. 2x 5 13+ ≤ −

11. 3 6x 1− ≤ − 12. 17 4x 11≥ + 13. x 4 3x 2− − > − 14. 3x 5 7x 9+ < − − 15. x 3 2 ( x 4 )+ ≤ − 16. 2x 10 7 ( x 1)+ ≥ + 17. x 4 2 ( x 8 )− + < − − 18. x 6 ( 2x 4 )− + > − + 19. 4x 3 8x 11+ ≤ − 20. 13 5y 7y 29− > +

10

11

12

• rad

ius