Download Solving Linear Equations Chapter Questions 1. What are inverse

Solving Linear Equations Chapter Questions
1. What are inverse operations? Name them.
2. How do you solve equations?
3. What do you do when an equation has variables on both sides?
4. How do you transform equations? Why would you want to?
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Solving Equations Chapter Problems
Inverse Operations
Classwork
1. Name the inverse operation needed to solve for the variable.
a. x + 9 = 17
b. y – 8 = 5
c. m + 5 = 21
w
 12
6
d.
e. 9v = 108
Homework
2. Name the inverse operation needed to solve for the variable.
a. t – 18 = 54
b. 14x = 228
c. m + 19 = 51
d. 11b = 66
m
2
4
e.
One Step Equations
Classwork
3. Solve.
a.
b.
c.
d.
e.
f.
g.
n + 7 = 20
x + 9 = -8
a – 15 = 27
y – 21 = -15
50 + w = 92
-4 + m = 18
m
 16
8
h. 30 = 12m
i. -5m = 25
j.
1
t  12
6
k.
-10c = -80
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l. n – (-6)= 12
m. -82 + x = -20
r
5
2
n.
Homework
4. Solve.
a.
b.
c.
d.
e.
f.
g.
n + 9 = 13
-14 + b = 21
z – 18 = -14
-7 + g = -12
19 = 15 + y
b + (-4) = 13
q
 33
3
h. -18x = -360
i. x – 11 = 4
j.
1
n  15
5
k. -15c = -75
l. -8 + r = 27
m. 19 + m = 3
n.
w
1
8
Two Step Equations
Classwork
Solve.
5. 7x – 2 = 26
6. ½ (m – 3) = 12
7. -6h – 6 = 30
8. 5x + 20 = -20
9. 3 = -3y – 15
10. -24 = 14y – 5
11. 7r – 5 = 10
12. 9 = 16y + 51
13. 13x + 6 = 6
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14.
x
 11  5
4
Homework
15. 2m – 8 = -28
16.
x
3  8
9
17. 12m + 20 = -40
x
 5  21
18. 3
19. 8r – 27 = -19
6
20.
k
 33
3
21. 15 = -4y – 9
22. 8w + 4 = -36
23. 4a – 15 = -23
24. 44 = 5x - 6
Multi-Step Equations
Classwork
Solve.
25. 8s – (8 + 6s) = 20
26. 34 = 2x + 8(x + 3)
27.
3
( x  9)  15
4
2
(m  8)  4
28. 3
29. 35 = 22x – 12x + 5
30. 6(b + 8) = 54
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31. 99 = 33x + 3(3x + 5)
32. –t + (5t – 7) = -5
33. 21 – 3(2 – w) = -12
34. 9 = 8b – (2b – 3)
Homework
Solve.
35. 6(m + 4) – 2m = -8
36. 44 = 4(8 + h)
37.
3
(8t  4)  2
4
1
0  (10h  15)  h
5
38.
39. 3(5 – t) – 4t = 18
40. 2(y - 5) = 16
41. 0.1(h + 20) = 3
3z
45
42. 8
43. 8.6 = 6j + 4j
44. 12z – (4z + 6) = 82
Variables on Both Sides
Classwork
Solve.
45. 18 – 5t = t
46. 3m – 6 = 5m + 8
47. 22w – 42 = 34 – 16w
48. r + 6 – 5r = 14 – 2r
49. 6x + 12 = 4x
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50. 4n – 14 = -16n + 26
51. y – 2y + 3 = 3 – y
52. 4u – 7 = u + 3(4 + u)
53. 4m – (8 – m) = 6 – 2m
54. 3b + 16 = 5b + 16 – 2b
Homework
Solve.
55. 2m = 24 + 3m
56. 5w – 17 = 12 – 5w
57. 2p – 9 = 5p + 12
58. 35 – y = 4y
59. 10x = 4x – 8x + 7
60. 2s + 16 = s - 25
61. 14 – (2c + 5) = -2c + 9
62. 20 – 16p = 4(5 – 4p)
63. 4n + 8 = 8 – 4n
64. 1.4h = 1.8h + 4.8 – 0.4h
More Equations
Classwork
65.
1
(6w  12)  6  2( w  2)
6
66. 6(6 – 2a) = -27a -
3
(-4a + 6)
2
67. 2b + 4(b – 6) = -2(2b – 14) + 98
68. 4g + 3(g – 2) = -5(g – 4) - g
69. -7 + 8(5 – 3s) = 3(7 – 9s)
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69A. The sum of the ages of the three Romano brothers is 63. If their ages can be represented as
consecutive integers, what is the age of the middle brother?
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
Homework
70.
2
(9 x  15)  17  3( x  12)
3
71. 2(3x – 4) = -2x + 40
72. 3(1 + 2x) – 4x = -(x + 30)
73. 8g + 6(g – 2) = -10(g – 4) – 2g
74. 12(3n – 7) + 8n = -2(4 – 3n)
74A. Arielle has a collection of grasshoppers and crickets. She has
561 insects in all. The number of grasshoppers is twice the number
of crickets. Find the number of each type of insect that she has.
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
Transforming Formulas
Classwork
75. Solve for w. A = lw
76. Solve for m.
t
vm
3
77. Solve for b.
16c  10b  2
78. Solve for h.
1
A  bh
2
79. Solve for
4
3
 . V   r3
Homework
80. Solve for l. P = 2l + 2w
81. Solve for c.
82. Solve for s.
p
bc
5
20 x  5s  8
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83. Solve for h.
V  2r 2 h
84. Solve for h. A 
1
(b1  b2 )h
2
85. The formula for the volume of a right circular cylinder is V = πr2h.
The value of h can be expressed as
πr 2
V 2
(1) π r
(3) V
(2)
V
(4) V – πr2
πr 2
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
86. If c = 2m + d, then m is equal to
c−d
d
(1)
(3) c −
2
2
(4) d − 2c
(2) c − d
2
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
Unit Review
Multiple Choice Questions
1. Name the inverse operation used to solve this equation:
x - 15 = -10
a. Multiplication
b. Division
c. Addition
d. Subtraction
2. Name the inverse operation used to solve this equation:
4s = 84
a. Multiplication
b. Division
c. Addition
d. Subtraction
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3. Name the inverse operation used to solve this equation:
f/4 = 2
a. Multiplication
b. Division
c. Addition
d. Subtraction
4. Name the inverse operation used to solve this equation:
-18 + x = 30
a. Multiplication
b. Division
c. Addition
d. Subtraction
5. Solve the equation: y + 17 = 29
a. y = 36
b. y = 12
c. y = -12
d. y = 11
6. Solve the equation: 2 - 20x = 162
a. x = -8.2
b. x = 8.2
c. x = 8
d. x = -8
7. Solve the equation: 4.3d = -288.1
a. d = -283.8
b. d = -292.4
c. d = 67
d. d = -67
8. Solve the equation: 4.0 + 8.7k - 2.6 = 2
a. k = 14.5
b. k = -14.5
c. k = 0.39
d. k = 5.22
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9. Solve the equation: 5/7r - 2 = -1
a. r = 7/5
b. r = 5/7
c. r = -4 1/5
d. r = -2 1/7
10. Solve the equation: 3/8 + 1/2w - 4 = 3
a. w = 13 1/4
b. w = 1 13/14
c. w = 106/4
d. w = 13
11. Solve the equation: -3(2u + 5) + 3.5u = -1u
a. u = 10
b. u = -10
c. u = 4
d. u = -4
12. Solve the equation: -4a = 14a - 12(4a+ 10)
a. a = 10
b. a = 4
c. a = -4
d. a = -10
13. Solve the equation: 2(x + 6) = 2(-x + 6.5)
a. x = 13
b. x = 0.4
c. x = 4
d. x = 1/4
14. Solve the equation: 5t = 2 - t
a. t = -6
b. t = -3
c. t = 3
d. t = 6
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Short Constructed Response Questions
15. 8x - 18 = 46
x=
16. 27.5 = 2.5q + 1q -4
q=
17. -3e + 8 = -1
e=
18. 2/5y + y - 8 = 11
y=
19. -14.5b - 3 + 0.5b = 18
b=
20. -6(2m +1) = 3m + 54
m=
21. 2x - 4 - 2x = -(8x + 2)
x=
22. 3(2x + 3) = 2(x - 4)
x=
23. -5( -10 +8v) = -30
v=
24. 1/6c + 0.5 + 5/6c = 1
c=
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Extended Constructed Response Questions
25. The clerk at the bank desk says there is an initial charge of $50.00 to open up a bank account at
the Sunny Farms Bank. He then explains that after, every account added on will cost an
additional $15.50 each. The Smith Family is thinking of opening an account for the family.
a. Write an equation that represents the cost to open accounts for the family members.
b. What is the greatest amount of family members that could open a bank account
without exceeding a fee of $500?
c. How much money would it cost if Mom Smith, Dad Smith, Sister Smith, and Brother
Smith want to open an account, and Mom Smith has a special discount coupon of
15% off the final price?
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26. The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of
$6.00 for every data one goes over a month. The Cellular Phone Service Company has a
monthly fee of $80 and an additional charge of $10.00 for every data one goes over. The Gomez
family is deciding which of these two phone providers to subscribe to.
a. Write an equation that represents the cost of each phone company’s monthly fee. Let
p = cost.
b. For what number of data over will the total monthly fee for both companies be the
same?
c. The Gomez family’s daughter went over 6 data last month. Which phone service will
save the Gomez family the more if the daughter repeats this bad habit next month?
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Answer Key
1.
a. Subtraction
b. Addition
c. Subtraction
d. Multiplication
e. Division
2.
a. Addition
b. Division
c. Subtraction
d. Division
e. Multiplication
3.
a. 13
b. -17
c. 42
d. 6
e. 42
f. 22
g. 128
h. 2.5
i. -5
j. 72
k. 8
l. 6
m. 62
n. -10
4.
a. 4
b. 35
c. 4
d. -5
e. 4
f. 17
g. 99
h. 20
i. 15
j. 75
k. 5
l. 35
m. -16
n. -8
5. 4
6. 27
7. -6
8. -8
9. -6
10. -19/14
11. 15/7
12. -21/8
13. 0
14. 24
15. -10
16. 99
17. -5
18. -48
19. 1
20. 81
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21. -6
22. -5
23. -2
24. 10
25. 14
26. 1
27. 11
28. 14
29. 3
30. 1
31. 2
32. ½
33. -9
34. 1
35. -8
36. 3
37. 1/6
38. -1
39. -3/7
40. 13
41. 10
42. 24
43. 0.86
44. 11
45. 3
46. -7
47. 2
48. -4
49. -6
50. 2
51. All Real Numbers
52. No Solution
53. 2
54. All Real Numbers
55. -24
56. 2.9
57. -7
58. 7
59. ½
60. -41
61. All Real Numbers
62. All Real Number
63. 0
64. No Solution
65. 4
66. -5
67. 15
68. 2
69. -4 69A. 21
70. 7
71. 6
72. -11
73. 2
74. 2
74A. Crickets: 187;
Grasshoppers: 374
75. A/l
76. 3t-v
77. (16c-2)/10
78. 2A/b
79.
80.
81.
82.
83.
84.
85.
86.
(3V)/(4r3)
(P-2w)/2
5p-b
(20x-8)/5
V/2r2
2A/(b1+b2)
2
1
Unit Review
1. c
2. b
3. a
4. c
5. b
6. d
7. d
8. a
9. a
10. a
11. b
12. c
13. d
14. c
15. x = 8
16. q = 9
17. e = 3
18. y = 13 4/7
19. b = - 3/2
20. m = -4
21. x = 1/4
22. x = -9/2
23. v = 2
24. c = 0.5
25. a. cost = $50.00 +
$15.50x
b. 29 members
c. $95.20
26. a. p = $100.00 +$6.00x
p= $80.00 +$10.00x
b. 5 data
c. Rainbow Phone
Service
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