chapter foundations of algebra 1 solutions key
TRANSCRIPT
Foundations of AlgebraSolutions Key
Are You reAdY?
1. E 2. A
3. C 4. D
5. (7 - 3) ÷ 2 = 4 ÷ 2 = 2
6. 4 · 6 ÷ 3 = 24 ÷ 3 = 8
7. 12 - 3 + 1 = 9 + 1 = 10
8. 2 · 10 ÷ 5 = 20 ÷ 5 = 4
9. 125 ÷ 5 2 = 125 ÷ 25 = 5
10. 7 · 6 + 5 · 4 = 42 + 20 = 62
11. -15 + 19 = 4
12. -6 - (-18) = -6 + 18 = 12
13. 6 + (-8) = 6 - 8 = -2
14. -12 + (-3) = -12 - 3 = -15
15. 1 __ 4 + 2 __
3
= 3 ___ 12
+ 8 ___ 12
= 3 + 8 _____ 12
= 11 ___ 12
16. 1 1 __ 2 - 3 __
4
= 6 __ 4 - 3 __
4
= 6 - 3 _____ 4
= 3 __ 4
17. 3 __ 8 + 2 __
3
= 9 ___ 24
+ 16 ___ 24
= 9 + 16 ______ 24
= 25 ___ 24
18. 3 __ 2 - 2 __
3
= 9 __ 6 - 4 __
6
= 9 - 4 _____ 6
= 5 __ 6
19. 2x + 3 = 2(7) + 3 = 14 + 3 = 17
20. 3n - 5 = 3(7) - 5 = 21 - 5 = 16
21. 13 - 4a = 13 - 4(2) = 13 - 8 = 5
22. 3y + 5 = 3(5) + 5 = 15 + 5 = 20
23. 4(0.75) + 6(0.60) 24. 13ℓ
25. Possible answer: a number plus 2 times itself
VAriAbles And expressions
CheCk it OUt!
1. Possible answers given
a. 4 decreased by n; n less than 4
b. the sum of 9 and q; q added to 9
c. the quotient of t and 5; t divided by 5
d. the product of 3 and h; 3 times h.
2a. 65t b. m + 5
c. 32d 3a. mn = 3 · 2 = 6
b. p - n= 9 - 2 = 7
c. p ÷ m= 9 ÷ 3 = 3
4a. 63s b. 63(12) = 756 bottles;63(25) = 1575 bottles;63(50) = 3150 bottles
think and disCUss
1. addition - increase by, sum of; subtraction - decreased by, difference of; multiplication - multiplied by, product of; division - divided by, quotient of
2. Both types of expressions may contain numbers and operation. Algebraic expressions may also contain variables.
3. Words
Addition
Subtraction
Multiplication
Division
3 more than x
1 less than y
The product of 2 and n
The quotient of x and 4
x + 3
y - 1
2n
Algebra
x ÷ 4
eXeRCisesguided practice
1. variable
2–9. Possible answers given
2. 5 less than n; n decreased by 5
3. the quotient of f and 3; f divided by 3
4. c increased by 15; the sum of c and 15
5. 9 decreased by y; y less than 9
6. one-twelfth x; the quotient of x and 12
7. the sum of t and 12; t increased by 12
8. the product of 8 and x; 8 groups of x
9. x decreased by 3; the difference of x and 3
10. 45h 11. w + 4
12. a - c= 3 - 2 = 1
13. ab 3 · 4 = 12
14. b ÷ c4 ÷ 2 = 2
15. ac3 · 2 = 6
16a. 0.5d b. 0.5d 0.5(2) = 1 0.5(4) = 2 0.5(10) = 5
practice and problem Solving
17. the product of 5 and p; 5 groups of p
18. 4 decreased by y; the difference of 4 and y
19. the sum of 3 and x; 3 increased by x
20. the product of 3 and y; 3 times y
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21. negative 3 times s; the product of negative 3 and s
22. the quotient of r and 5; one-fifth r
23. 14 decreased by t; the difference of 14 and t
24. the sum of x and 0.5; x increased by 0.5
25. t + 20 26. 8n
27. 6 - 5 = 1 28. 5 + 3 = 8
29. 6 ÷ 3 = 2 30. 5 · 6 = 30
31a. h - 40
b. h - 40 (40) - 40 = 0 (44) - 40 = 0 (48) - 40 = 0 (52) - 40 = 0
32. To evaluate an expression is to find its value. To do this, substitute values for the variables and perform all the indicated operations.
33. 2x; possible answer: Jim has twice as many aunts as Carly, who has x aunts.
34. 17 - b; possible answer: Sarah started with 17 apples, but lost b of them.
35. y + 10; possible answer; April had y CDs and then got 10 more.
36a. air pressure
b. depth below the water in feet.
c. 14.7 + 0.445d = 14.7 + 0.445(8) = 14.7 + 3.56 = 18.26 psi
37. A = ℓ · wA = 9wA = 9(1) = 9 in 2 A = 9(8) = 72 in 2 A = 9(9) = 81 in 2 A = 9(11) = 99 in 2
38a. P = 2ℓ + 2w b. P = 2ℓ + 2w = 2(14) + 2(8) = 28 + 16 = 44 cm
c. A = ℓ · w or ℓw d. A = ℓw = (8)(14) = 112 cm 2
39. x x + 12
1 (1) + 12 = 13
2 (2) + 12 = 14
3 (3) + 12 = 15
4 (4) + 12 = 16
40. x 10x1 10(1) = 10
5 10(5) = 50
10 10(10) = 100
15 10(15) = 150
41. x x ÷ 2
12 (12) ÷ 2 = 6
20 (20) ÷ 2 = 10
26 (26) ÷ 2 = 13
30 (30) ÷ 2 = 15
42a. Let p represent the weight of an object on Earth in pounds; 0.38p
b. p = 120 + 44 = 164 0.38p = 0.38(164) = 62.31 lbs
43a. 47.84 + m b. 58.53 - s
44. Both algebraic and numerical expressions contain numbers and operations, but algebraic expressions also contain variables.
Verbal algebraic x = 12 x = 14x reduced
by 5 x - 5 12 - 5 = 7 14 - 5 = 9
45. 7 more than x x + 7 12 + 7 = 19 14 + 7 = 21
46. The quotient of x and 2
x _ 2 12
__ 2 = 6 14 __
2 = 7
47. The sum of x and 3 x + 3 12 + 3 = 15 14 + 3 = 17
teSt prep
48. C; b fewer than 3. 49. F; 12 - 5
50. B; Sarah has driven the difference of 25 and x.
challenge and extend
51. 2ab = 2(6)(3) 52. 2x + y = 2(4) + (5)= 36 = 8 + 5 = 13
53. 3x ÷ 6y = 3(6) ÷ 6(3)= 1
54. Let h represent the number of hours used in a month when h is more than 20 hours.9.95 + 0.50(h - 20)= 9.95 + 0.50(35 - 20)= 9.95 + 0.50(15) = $17.45
solVing equAtions bY Adding or subtrActing
CheCk it OUt!
1a. n - 3.2 = 5.6 ______ + 3.2 _____ + 3.2 n = 8.8
b. -6 = k - 6 ___ +6 _____ + 6 0 = k
c. 16 = m - 9 ___ + 9 _____ + 9 25 = m
2a. d + 1 __ 2 = 1
_____
- 1 __ 2
____ - 1 __
2
d = 1 __ 2
b. -5 = k + 5 ___ - 5 _____ - 5 -10 = k
c. 6 + t = 14 _______ - 6 ___ - 6 t = 8
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3a. -2.3 + m = 7 _________ + 2.3 _____ + 2.3 m = 9.3
b. - 3 __ 4 + z = 5 __
4
________
+ 3 __ 4
____ + 3 __
4
z = 2
c. -11 + x = 33 ________ + 11 ____ + 11 x = 44
4. a + r = 220 a + 185 = 220 _______ - 185 _____ -185 a = 35 The age of a person who has a maximum heart rate
of 185 beats per minute is 35 years old.
think and disCUss
1. Possible answer: If a scale is balanced, then you can add or remove the same weight on both sides without affecting the balance. Similarly, in an equation, the Addition and Subtraction Properties of Equality say that you can add or subtract the same value on both sides without affecting the equality.
2. Properties of Equality
x - 6 = 2 x = 8
+ 4 + x = -1
x = -5
-
eXeRCisesguided practice
1. Possible answer: The solution of an equation is a number. It is a value for the variable that works in the equation.
2. s - 5 = 3 _____ + 5 ___ + 5 s = 8
3. 17 = w - 4 ___ + 4 _____ + 4 21 = w
4. k - 8 = -7 _____ + 8 ___ + 8 k = 1
5. x - 3.9 = 12.4 ______ + 3.9 _____ + 3.9 x = 16.3
6. 8.4 = y - 4.6 _____ + 4.6 _______ + 4.6 13 = y
7. 3 __ 8 = t - 1 __
8
____
+ 1 __ 8
_____ + 1 __
8
1 __ 2 = t
8. t + 5 = -25 ____ - 5 ____ - 5 t = -30
9. 9 = s + 9 ___ - 9 _____ - 9 0 = s
10. 42 = m + 36 ____ - 36 _______ - 36 6 = m
11. 2.8 = z + 0.5 _____ - 0.5 _______ - 0.5 2.3 = z
12. b + 2 __ 3 = 2
_____
- 2 __ 3
____ - 2 __
3
b = 4 __ 3
13. n + 1.8 = 3 ______ - 1.8 _____ - 1.8 n = 1.2
14. -10 + d = 7 ________ + 10 ____ + 10 d = 17
15. 20 = -12 + v ____ + 12 ________ + 12 32 = v
16. -46 + q = 5 ________ + 46 ____ + 46 q = 51
17. 2.8 = -0.9 + y _____ + 0.9 ________ + 0.9 3.7 = y
18. - 2 __ 3 + c = 2 __
3
________
+ 2 __ 3
____ + 2 __
3
c = 4 __ 3
19. - 5 __ 6
+ p = 2
________
+ 5 __ 6
____
+ 5 __ 6
p = 17 ___ 6
20. Let w represent the weight of the original diamond. w - 45 = 67 ______ + 45 ____ + 45 w = 112 The original diamond weighed 112 carats.
Possible answer: The weight of the diamond was reduced by about 50 carats, resulting in a diamond that weighed about 70 carats. So the original weight will be close to 50 + 70 = 120 carats. So 112 carats is reasonable.
practice and problem Solving
21. 1 = k - 8 ___ + 8 _____ + 8 9 = k
22. u - 15 = -8 ______ + 15 ____ + 15 u = 7
23. x - 7 = 10 _____ + 7 ___ + 7 x = 17
24. -9 = p - 2 ___ + 2 _____ + 2 -7 = p
25. 3 __ 7 = p - 1 __
7
____
+ 1 __ 7
______ + 1 __
7
4 __ 7 = p
26. q - 0.5 = 1.5 ______ + 0.5 _____ + 0.5 q = 2
27. 6 = t - 4.5 _____ + 4.5 ______ + 4.5 10.5 = t
28. 4 2 __ 3
= r - 1 __ 3
____
+ 1 __ 3
_____
+ 1 __ 3
5 = r
29. 6 = x - 3 ___ + 3 _____ + 3 9 = x
30. 1.75 = k - 0.75 ______ + 0.75 ________ + 0.75 2.50 = k
31. 19 + a = 19 ________ - 19 ____ - 19 a = 0
32. 4 = 3.1 + y _____ - 3.1 ________ - 3.1 0.9 = y
33. m + 20 = 3 ______ - 20 ____ - 20 m = -17
34. -12 = c + 3 ___ - 3 _____ - 3 -15 = c
35. v + 2300 = -800 ________ - 2300 ______ - 2300 v = -3100
36. b + 42 = 300 ______ - 42 ____ - 42 b = 258
37. 3.5 = n + 4 _____ - 4 _____ - 4 -0.5 = n
38. b + 1 __ 2
= 1 __ 2
_____
- 1 __ 2
____
- 1 __ 2
b = 0
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39. x + 5.34 = 5.39 _______ - 5.34 ______ - 5.34 x = 0.05
40. 2 = d + 1 __ 4
____
- 1 __ 4
______ - 1 __
4
7 __ 4 = d
41. -12 + f = 3 ________ + 12 ____ + 12 f = 15
42. -9 = -4 + g ___ + 4 _______ + 4 -5 = g
43. -1200 + j = 345 __________ + 1200 ______ + 1200 j = 1545
44. 90 = -22 + a ____ + 22 ________ + 22 112 = a
45. 26 = -4 + y ___ + 4 _______ + 4 30 = y
46. 1 3 __ 4 = - 1 __
4 + w
____
+ 1 __ 4
________ + 1 __
4
2 = w
47. - 1 __ 6 + h = 1 __
6
________
+ 1 __ 6
____ + 1 __
6
h = 1 __ 3
48. -5.2 + a = -8 ________ + 5.2 _____ + 5.2 a = -2.8
49. Let a represent the amount in Luis’s acount before the deposit.
a + 500 = 4732 _______ - 500 _____ - 500 a = 4232 Luis had $4232 in his account before the deposit.
Possible answer: Luis deposited $500 and now has about $4700. So the original amount will be close to
4700 - 500 = 4200. So $4232 is a reasonable answer.
50. Solution B is incorrect. The Addition Property of Equality was used.
51. x - 10 = 12 ______ + 10 ____ + 10 x = 22
52. x - 13 = 7 ______ + 13 ____ + 13 x = 20
53. x + 8 = 16 _____ - 8 ___ - 8 x = 8
54. x - 3 = -8 _____ + 3 ___ + 3 x = -5
55. 5 + x = 6 _______ - 5 ___ - 5 x = 1
56. x - 2 = -5 _____ + 2 ___ + 2 x = -3
57. x - 4 = 9 _____ + 4 ___ + 4 x = 13
58. Let a represent the average depth of the Atlantic Ocean.
a + 30,246 = 43,126 _________ - 30,246 ________ - 30,246 a = 12,880 The average depth of the Atlantic Ocean is
12,880 ft.
Possible answer: The greatest depth is about 30,000 ft. The sum of this number and the average is about 43,000 ft. So the average will be close to
43,000 - 30,000 = 13,000. So 12,800 ft is a reasonable answer.
59. Let m represent the amount of money the band still needs.
m + 560 = 1680 _______ - 560 _____ - 560 m = 1120 Helene’s band still needs to raise $1120.
Possible answer: The band needs about $1700 and they have raised about $600. So the amount they need will be close to 1700 - 600 = 1100. So $1120 is a reasonable answer.
60. Let c represent the cost of the car. c - 1500 = 2600 ________ + 1500 ______ + 1500 c = 4100 The car cost $4100.
Possible answer: The total cost should be more than the down payment and more than the loan amount, so $4100 is a reasonable answer.
61. 63 + x = 90 ________ - 63 ____ - 63 x = 27
62. 42 + x = 90 ________ - 42 ____ - 42 x = 48
63. x + 15 = 90 ______ - 15 ____ - 15 x = 75
64a. 2000 acres; possible answer: The fire should cover twice as much area in 2 days as it does in 1, so multiply 2 by 1000 and the answer is 2000 acres.
b. 5000 acres; multiply 5 days by 1000 acres per day.
c. Divide 780 by 7.
65. Let h represent the highest score. h - 47 = 28 ______ + 47 ____ + 47 h = 75 The highest score is 75.
Possible answer: The range is about 30 and the lowest score is about 50. So the highest score will be close to 30 + 50 = 80. So 75 is a reasonable answer.
66. Possible answer: If you add 5 years to Sue’s age, you get her cousin’s age. Her cousin is 25. How old is Sue? x represents Sue’s age.
x + 5 = 25 _____ - 5 ___ - 5 x = 20 Sue is 20 years old.
67. Possible answer: greater than 10 because you will add a positive number to both sides
teSt prep
68. A: 32 is being subtracted from x so the situation must decrease by 32. Choice A has a withdrawal of 32.
69. J: Since 8 + 8 = 16, J is an equation for which a = 8 is a solution.
70a. g - 18 = 22 b. $40 g - 18 = 22 ______ + 18 ____ + 18 g = 40
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challenge and extend
71. 3 1 __ 5 + b = 4 __
5
________
- 3 1 __ 5
_____ - 3 1 __
5
b = - 12 ___ 5
72. x - 7 __ 4 = 2 __
3
_____
+ 7 __ 4
____ + 4 __
7
x = 29 ___ 12
73. x + 7 __ 4 = 2 __
3
______
- 7 __ 4
_____ - 7 __
4
x = - 13 ___ 12
74. x - 4 __ 9 = 4 __
9
_____
+ 4 __ 9
____ + 4 __
9
x = 8 __ 9
75. p - 4 = 2 _____ + 4 ___ + 4 p = 6
5p - 20 = 5(6) - 20 = 30 - 20 = 10
76. t + 6 = 21 ____ - 6 ___ - 6 t = 15
-2t = -2(15) = -30
77. x + 3 = 15 _____ - 3 ___ - 3 x = 12
18 + 6x = 18 + 6(12) = 18 + 72 = 90
78. 2 + n = -11 _______ - 2 ____ - 2 n = -13
6n = 6(-13) = -78
solVing equAtions bY multiplYing or diViding
CheCk it OUt!
1a. p __
5 = 10
(5) ( p __
5 ) = (5)(10)
p = 50
b. -13 = y __
3
(3)(-13) = (3) ( y __
3 )
-39 = y
c. c __ 8 = 7
(8) ( c __ 8 ) = (8)(7)
c = 56
2a. 16 = 4c
16 ___ 4 = 4c ___
4
4 = c
b. 0.5y = -10
0.5y
____ 0.5
= -10 ____ 0.5
y = -20
c. 15k = 75
15k ____ 15
= 75 ___ 15
k = 5
3a. - 1 __ 4 = 1 __
5 b
(5) (- 1 __ 4 ) = (5) ( 1 __
5 b)
- 5 __ 4 = b
b. 4j
__ 6 = 2 __
3
( 6 __ 4 ) 4 __
6 j = ( 6 __
4 ) 2 __
3
j = 1
c. 1 __ 6 w = 102
(6) ( 1 __ 6 w) = (6)(102)
w = 612
4. d __ 3 = h
45 ___ 3 = h
15 = h The plane was 15,000 ft high when it began its
descent.
think and disCUss
1. Possible answer: All four properties tell you that if you perform the same operation on both sides of the equation, the equality will still hold.
2. Properties of Equality
×
6x = -12
÷
x = 40
= 4 x _ 10
x = -2
eXeRCisesguided practice
1. k __ 4 = 8
(4) ( k __ 4 ) = (4)(8)
k = 32
2. z __ 3
= -9
(3) ( z __ 3
) = (3)(-9)
z = -27
3. -2 = w ___ -7
(-7)(-2) = (-7) ( w ___ -7
)
14 = w
4. 6 = t ___ -5
(-5)(6) = (-5) ( t ___ -5
)
-30 = t
5. g ___
1.9 = 10
(1.9) ( g ___
1.9 ) = (1.9)(10)
g = 19
6. 2.4 = b __ 5
(5)(2.4) = (5) ( b __ 5
)
12 = b
7. 4x = 28
4x ___ 4 = 28 ___
4
x = 7
8. -64 = 8c
-64 ____ 8
= 8c ___ 8
-8 = c
9. -9j = -45
-9j
___ -9
= -45 ____ -9
j = 5
10. 84 = -12a
84 ____ -12
= -12a _____ -12
-7 = a
11. 4m = 10
4m ___ 4 = 10 ___
4
m = 2.5
12. 2.8 = -2h
2.8 ___ -2
= -2h ____ -2
-1.4 = h
13. 1 __ 2 d = 7
(2) ( 1 __ 2 d) = (2)(7)
d = 14
14. 15 = 5 __ 6
f
( 6 __ 5
) (15) = ( 6 __ 5
) ( 5 __ 6
f)
18 = f
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15. 2 __ 3 s = -6
( 3 __ 2 ) ( 2 __
3 s) = ( 3 __
2 ) (-6)
s = -9
16. 9 = - 3 __ 8 r
(- 8 __ 3 ) (9) = (- 8 __
3 ) (- 3 __
8 r)
-24 = r
17. 1 ___ 10
= ( 4 __ 5 ) y
( 5 __ 4 ) 1 ___
10 = ( 5 __
4 ) 4 __
5 y
1 __ 8 = y
18. 1 __ 4 v = - 3 __
4
(4) ( 1 __ 4 v) = (4) (- 3 __
4 )
v = -3
19. Let c represent the cost per child. 16c = 192
16c ____ 16
= 192 ____ 16
c = 12 The cost per child is $12.
20. Let a represent the amount of vitamin C in an apple. 80 = 10a
80 ___ 10
= 10a ____ 10
8 = a There are 8 mg of vitamin C in an apple.
practice and problem Solving
21. x __ 2 = 12
(2) ( x __ 2 ) = (2)(12)
x = 24
22. -40 = b __ 5
(5)(-40) = (5) ( b __ 5 )
-200 = b
23. - j __
6 = 6
(-6) (- j __
6 ) = (-6)(6)
j = -36
24. - n __ 3 = -4
(-3) (- n __ 3 ) = (-3)(-4)
n = 12
25. - q __
5 = 30
(-5) (- q
__ 5 ) = (-5)(30)
q = -150
26. 1.6 = d __ 3
(3)(1.6) = (3) ( d __ 3 )
4.8 = d
27. v ___ 10
= 5.5
(10) ( v ___ 10
) = (10)(5.5)
v = 55
28. h ___ 8.1
= -4
(8.1) ( h ___ 8.1
) = (8.1)(-4)
h = -32.4
29. 5t = -15
5t __ 5 = -15 ____
5
t = -3
30. 49 = 7c
49 ___ 7 = 7c ___
7
7 = c
31. -12 = -12u
-12 ____ -12
= -12u _____ -12
1 = u
32. -7m = 63
-7m _____ -7
= 63 ___ -7
m = -9
33. -52 = -4c
-52 ____ -4
= -4c ____ -4
13 = c
34. 11 = -2z
11 ___ -2
= -2z ____ -2
-5.5 = z
35. 5f = 1.5
5f __ 5 = 1.5 ___
5
f = 0.3
36. -8.4 = -4n
-8.4 _____ -4
= -4n ____ -4
2.1 = n
37. 5 __ 2 k = 5
( 2 __ 5 ) ( 5 __
2 k) = ( 2 __
5 ) (5)
k = 2
38. -9 = 3 __ 4 d
( 4 __ 3 ) (-9) = ( 4 __
3 ) ( 3 __
4 ) d
-12 = d
39. - 5 __ 8 b = 10
(- 8 __ 5 ) (- 5 __
8 b) = (- 8 __
5 ) (10)
b = -16
40. - 4 __ 5 g = -12
(- 5 __ 4 ) (- 4 __
5 g) = (- 5 __
4 ) (-12)
g = 15
41. 4 __ 7 t = -2
( 7 __ 4 ) ( 4 __
7 t) = ( 7 __
4 ) (-2)
t = -3.5
42. - 4 __ 5 p = 2 __
3
(- 5 __ 4 ) (- 4 __
5 p) = (- 5 __
4 ) ( 2 __
3 )
p = - 5 __ 6
43. 2 __ 3 = - 1 __
3 q
(-3) ( 2 __ 3 ) = (-3) (- 1 __
3 q)
-2 = q
44. - 5 __ 8 = - 3 __
4 a
(- 4 __ 3 ) (- 5 __
8 ) = (- 4 __
3 ) (- 3 __
4 a)
5 __ 6 = a
45. Let s represent Alexandra’s salary before taxes.
7 ___ 10
s = 392
( 10 ___ 7 ) ( 7 ___
10 s) = ( 10 ___
7 ) (392)
s = 560 Alexandra’s salary before taxes is $560.
46. Let w represent the person’s weight on Earth.
1 __ 6 w = 16
(6) ( 1 __ 6 w) = (6)(16)
w = 96 The person weighs 96 lb on Earth.
Possible answer: The person’s weight on the Moon is about 15 lb. The answer will be close to 15 · 6 = 90. So 96 lb is reasonable.
47. Possible answer: The student divided both sides by 3 instead of multiplying both sides by 3.
x __ 3 = 15
(3) ( x __ 3 ) = (3)(15)
x = 45
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48. 4s = 36
4s ___ 4 = 36 ___
4
s = 9 in.
49. 4s = 84
4s ___ 4 = 84 ___
4
s = 21 in.
50. 4s = 100
4s ___ 4 = 100 ____
4
s = 25 yd
51. 4s = 16.4
4s ___ 4 = 16.4 ____
4
s = 4.1 cm
52. 5x = 45
5x ___ 5 = 45 ___
5
x = 9
53. -3x = 12
-3x ____ -3
= 12 ___ -3
x = -4
54. x __ 4 = 10
(4) ( x __ 4 ) = (4)(10)
x = 40
55. x __ 3 = -8
(3) ( x __ 3 ) = (3)(-8)
x = -24
56. Let x represent the total measure of all students’ heights.
x ___ 18
= 60
(18) ( x ___ 18
) = (18)(60)
x = 1080 The total measure of all students’ heights is 1080 in.
57. Let h represent the number of hours Lisa worked each week.
6.25h = 50
6.25h _____ 6.25
= 50 ____ 6.25
h = 8 Lisa worked 8 hours each week.
58. Greater than 4; you are multiplying 4 by a positive number greater than 1.
59. Let m represent the number of minutes Dion was charged for.
0.05m = 13.80
0.05m ______ 0.05
= 13.80 _____ 0.05
m = 276 Dion was charged for 276 minutes.
Possible answer: Dion’s calls cost $0.05/min. If he talked for 300 min, the cost would be 300(0.05) = $15. This is close to the cost given in
the problem, $13.80. So 276 min is reasonable.
60. Let c represent the amount of caffeine in a 12 oz caffeinated soft drink.
5c = 184
5c ___ 5 = 184 ____
5
c ≈ 37 There are about 37 mg of caffeine in a 12 oz
caffeinated soft drink.
Possible answer: The amount of caffeine in the soft
drink should be about 200 ____ 5 = 40 mg. So 37 mg is
reasonable.
61. 8y = 4x 8y = 4(-4) 8y = -16
8y
___ 8 = -16 ____
8
y = -2
62. 8y = 4x 8y = 4(-2) 8y = -8
8y
___ 8 = -8 ___
8
y = -1
63. 8y = 4x 8y = 4(0) 8y = 0
8y
___ 8 = 0 __
8
y = 0
64. 8y = 4x 8y = 4(2) 8y = 8
8y
___ 8
= 8 __ 8
y = 1
65a. number of data values
b. mean
c. mean = sum of data values __________________ number of data values
96.21 = x _____ 1926
(1926)(96.21) = (1926) ( x _____ 1926
)
185,300 acres ≈ x Possible answer: There were about 1900 fires
and the mean acreage burned was about 100. So the total acres burned will be close to 1900(100) = 190,000. So 185,300 is reasonable.
66. m __ 6 = 1
(6) ( m __ 6 ) = (6)(1)
m = 6
67. 4x = 28
4x ___ 4
= 28 ___ 4
x = 7
68. 1.2h = 14.4
1.2h ____ 1.2
= 14.4 ____ 1.2
h = 12
69. 1 __ 5
x = 121
(5) ( 1 __ 5
x) = (5)(121)
x = 605
70. 2w = 26
2w ___ 2 = 26 ___
2
w = 13
71. 4b = 3 __ 4
( 1 __ 4 ) (4b) = ( 1 __
4 ) ( 3 __
4 )
b = 3 ___ 16
72. 5y = 11
5y
___ 5 = 11 ___
5
y = 11 ___ 5
73. n ___ 1.9
= 3
(1.9) ( n ___ 1.9
) = (1.9)(3)
n = 5.7
74. Let m represent the mean weight of an adult male mouse.
16m = 480
16m ____ 16
= 480 ____ 16
m = 30 The mean weight of an adult male mouse is 30 g.
Possible answer: An adult male rat weighs about 500 g, and this is about 20 times the weight of an adult mouse. So the mouse will weigh
close to 500 ____ 20
= 25 g. So 30 g is reasonable.
7 Holt McDougal Algebra 1
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75. Let g represent the average weight of a gerbil at birth.
2 __ 3 g = 2
( 3 __ 2 ) ( 2 __
3 g) = ( 3 __
2 ) (2)
g = 3 The average weight of a gerbil at birth is 3 g.
Possible answer: A hamster weighs 2 g at birth, so the gerbil’s weight will be greater than 2. So 3 g is reasonable.
76. Possible answer: Ryan has 3 times as many baseball cards as David. Ryan has 42 cards. How many cards does David have?
3x = 42
3x ___ 3 = 42 ___
3
x = 14 This represents the number of cards that David has.
teSt prep
77. D; Since situation D says “Mattie had 2 more,” the situation involves addition. Since the given equation does not contain addition, D cannot represent the equation.
78. J; Since x is multiplied by 3, the first step is to divide both sides by 3. Therefore, equation J is correct.
79. B; There are 540° in a pentagon and 5 angles. If x is the size of each angle, then 5 angles must add to 540°. Therefore 5x = 540 is correct.
80. H; Since 10 ___ 2 = 5, m = 10 is a solution for equation
H.
81a. 6c = 4.80; 6 is the number of cans of cat food; c is the cost per can; $4.80 is the total cost.
b. $0.80 6c = 4.80
6c ___ 6 = 4.80 ____
6
c = 0.80One can of cat food costs $0.80.
challenge and extend
82. (3 1 __ 5 ) b = 4 __
5
16 ___ 5 b = 4 __
5
( 5 ___ 16
) 16 ___ 5 b = ( 5 ___
16 ) 4 __
5
b = 1 __ 4
83. (1 1 __ 3 ) x = 2 2 __
3
4 __ 3 x = 8 __
3
( 3 __ 4 ) 4 __
3 x = ( 3 __
4 ) 8 __
3
x = 2
84. (5 4 __ 5 ) x = -52 1 __
5
29 ___ 5 x = - 261 ____
5
( 5 ___ 29
) 29 ___ 5 x = ( 5 ___
29 ) (- 261 ____
5 )
x = -9
85. (-2 9 ___ 10
) k = -26 1 ___ 10
-29 ____ 10
k = - 261 ____ 10
(- 10 ___ 29
) (- 29 ___ 10
k) = (- 10 ___ 29
) (- 261 ____ 10
)
k = 9
86. (1 2 __ 3 ) w = 15 1 __
3
5 __ 3 w = 46 ___
3
( 3 __ 5 ) 5 __
3 w = ( 3 __
5 ) 46 ___
3
w = 46 ___ 5
87. (2 1 __ 4 ) d = 4 1 __
2
9 __ 4 d = 9 __
2
( 4 __ 9 ) 9 __
4 d = ( 4 __
9 ) 9 __
2
d = 2
88. 2p = 4
2p
___ 2 = 4 __
2
p = 2
6p + 10 = 6(2) + 10 = 12 + 10 = 22
89. 6t = 24
6t __ 6 = 24 ___
6
t = 4
-5t = -5(4) = -20
90. 3x = 15
3x ___ 3 = 15 ___
3
x = 5
12 - 4x = 12 - 4(5) = 12 - 20 = -8
91. n __ 2 = -11
(2) ( n __ 2 ) = 2(-11)
n = -22
6n = 6(-22) = -132
92. a 93. Multiply both sides by a.
94a. d = rt
400 = 25t
400 ____ 25
= 25t ___ 25
16 = t
b. d = rt
400 = 50t
400 ____ 50
= 50t ___ 50
8 = t
c. t is divided in half (from 16 to 8).
d. t is divided in half.
solVing two-step And multi-step equAtions
CheCk it OUt!
1a. -4 + 7x = 3 ________ + 4 ___ + 4 7x = 7
7x ___ 7 = 7 __
7
x = 1
b. 1.5 = 1.2y - 5.7 _____ + 5.7 _________ + 5.7 7.2 = 1.2y
7.2 ___ 1.2
= 1.2y
____ 1.2
6 = y
8 Holt McDougal Algebra 1
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CS10_A1_MESK710372_C01.indd 8 3/30/11 10:30:49 PM
c. n __ 7 + 2 = 2
_____ - 2 ___ - 2
n __ 7 = 0
(7) ( n __ 7 ) = (7)(0)
n = 0
2a. 2x ___ 5 - 1 __
2 = 5
______
+ 1 __ 2
____ + 1 __
2
2x ___ 5 = 11 ___
2
( 5 __ 2 ) 2 __
5 x = ( 5 __
2 ) 11 ___
2
x = 55 ___ 4
b. 3 __ 4 u + 1 __
2 = 7 __
8
_______
- 1 __ 2
____ - 1 __
2
3 __ 4 u = 3 __
8
( 4 __ 3 ) 3 __
4 u = ( 4 __
3 ) 3 __
8
u = 1 __ 2
c. 1 __ 5 n - 1 __
3 = 8 __
3
______
+ 1 __ 3
____ + 1 __
3
1 __ 5 n = 3
(5) ( 1 __ 5 n) = (5)(3)
n = 15
3a. 2a + 3 - 8a = 8 2a - 8a + 3 = 8 -6a + 3 = 8 ________ - 3 ___ - 3 -6a = 5
-6a ____ -6
= 5 ___ -6
a = - 5 __ 6
b. -2(3 - d) = 4 (-2)(3) + (-2)(-d) = 4 -6 + 2d = 4 ________ + 6 ___ + 6 2d = 10
2d ___ 2 = 10 ___
2
d = 5
c. 4(x - 2) + 2x = 40 (4)(x) + (4)(-2) + 2x = 40 4x - 8 + 2x = 40 4x + 2x - 8 = 40 6x - 8 = 40 ______ + 8 ___ + 8 6x = 48
6x ___ 6 = 48 ___
6
x = 8
4. Let x represent Sara’s monthly fee. 12x + 15.95 = 735.95 __________ - 15.95 _______ - 15.95 12x = 720.00
12x ____ 12
= 720.00 ______ 12
x = 60.00 Sara’s monthly fee was $60.00.
5. 2x + 4 = -24 _____ - 4 ____ - 4 2x = -28
2x ___ 2 = -28 ____
2
x = -14
3x = 3(-14) = -42
think and disCUss
1. Possible answer: To solve 2x + 1 = 7, first subtract 1 from both sides and then divide both sides by 2. To solve 2x - 1 = 7, first add 1 to both sides and then divide both sides by 2.
2.
2x + 1 = 9 - 2 = 1
x = 4 x = 9
2x = 8
x _ 3
= 3 x _ 3
Solving Multi-Step Equations
eXeRCisesguided practice
1. 4a + 3 = 11 ______ - 3 ___ - 3 4a = 8
4a ___ 4 = 8 __
4
a = 2
2. 8 = 3r - 1 ___ + 1 ______ + 1 9 = 3r
9 __ 3
= 3r __ 3
3 = r
3. 42 = -2d + 6 ___ - 6 _______ - 6 36 = -2d
36 ___ -2
= -2d ____ -2
-18 = d
4. x + 0.3 = 3.3 ______ - 0.3 _____ - 0.3 x = 3
5. 15y + 31 = 61 _______ - 31 ____ - 31 15y = 30
15y
____ 15
= 30 ___ 15
y = 2
6. 9 - c = -13 - 9 - 9 -c = -22 (-1)(-c) = (-1)(-22) c = 22
7. x __ 6 + 4 = 15
_____ - 4 ___ - 4
x __ 6 = 11
6 ( x __ 6 ) = 6(11)
x = 66
8. 1 __ 3
y + 1 __ 4
= 5 ___ 12
______
- 1 __ 4
____
- 1 __ 4
1 __ 3
y = 1 __ 6
3 ( 1 __ 3
y) = 3 ( 1 __ 6
)
y = 1 __ 2
9 Holt McDougal Algebra 1
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9. 2 __ 7 j - 1 __
7 = 3 ___
14
______
+ 1 __ 7
____ + 1 __
7
2 __ 7 j = 5 ___
14
( 7 __ 2 ) 2 __
7 j = ( 7 __
2 ) 5 ___
14
j = 5 __ 4
10. 15 = a __ 3 - 2
___ + 2 _____ + 2
17 = a __ 3
3(17) = 3 ( a __ 3 )
51 = a
11. 4 - m __ 2 = 10
_______ -4 ___ - 4
- m __ 2 = 6
(-2) (- m __ 2 ) = (-2)(6)
m = -12
12. x __ 8 - 1 __
2 = 6
_____
+ 1 __ 2
____ + 1 __
2
x __ 8 = 13 ___
2
8 ( x __ 8 ) = 8 ( 13 ___
2 )
x = 52
13. 28 = 8x + 12 - 7x 28 = 8x - 7x + 12 28 = x + 12 ____ - 12 ______ - 12 16 = x
14. 2y - 7 + 5y = 0 2y + 5y - 7 = 0 7y - 7 = 0 ______ + 7 ___ + 7 7y = 7
7y
___ 7 = 7 __
7
y = 1
15. 2.4 = 3(m + 4) 2.4 = (3)(m) + (3)
(4) 2.4 = 3m + 12 ______ - 12 _______ - 12 -9.6 = 3m
-9.6 _____ 3 = 3m ___
3
-3.2 = m
16. 3(x - 4) = 48 (3)(x) + (3)(-4) = 48 3x - 12 = 48 _______ + 12 ____ + 12 3x = 60
3x ___ 3 = 60 ___
3
x = 20
17. 4t + 7 - t = 19 4t - t + 7 = 19 3t + 7 = 19 _____ - 7 ___ - 7 3t = 12
3t __ 3 = 12 ___
3
t = 4
18. 5(1 - 2w) + 8w = 15 (5)(1) + (5)(-2w) + 8w = 15 5 - 10w + 8w = 15 5 - 2w = 15 ________ - 5 ___ - 5 -2w = 10
-2w ____ -2
= 10 ___ -2
w = -5
19. Let x represent the number of daily bus passes Paul bought.
1.50x + 7 = 29.50 ________ - 7 ______ - 7 1.50x = 22.50
1.50x _____ 1.50
= 22.50 _____ 1.50
x = 15
Paul bought 15 daily bus passes.
20. 3x - 13 = 8 _______ + 13 ____ + 13 3x = 21
3x ___ 3 = 21 ___
3
x = 7
x - 4 = 7 - 4 = 3
21. 3(x + 1) = 7 (3)(x) + (3)(1) = 7 3x + 3 = 7 ______ - 3 ___ - 3 3x = 4
22. -3(y - 1) = 9
(-3)(y) + (-3)(-1) = 9 -3y + 3 = 9 _______ - 3 ___ - 3 -3y = 6
-3y
____ -3
= 6 ___ -3
y = -2
1 __ 2 y = 1 __
2 (-2)
= -1
23. 4 - 7x = 39 ________ - 4 ___ - 4 -7x = 35
-7x ____ -7
= 35 ___ -7
x = -5
x + 1 = -5 + 1 = -4
practice and problem Solving
24. 5 = 2g + 1 ___ - 1 ______ - 1 4 = 2g
4 __ 2 =
2g ___
2
2 = g
25. 6h - 7 = 17 _____ + 7 ___ + 7 6h = 24
6h ___ 6 = 24 ___
6
h = 4
26. 0.6v + 2.1 = 4.5 ________ - 2.1 _____ - 2.1 0.6v = 2.4
0.6v ____ 0.6
= 2.4 ___ 0.6
v = 4
27. 3x + 3 = 18 _____ - 3 ___ - 3 3x = 15
3x ___ 3 = 15 ___
3
x = 5
28. 0.6g + 11 = 5 ________ - 11 ____ - 11 0.6g = -6
0.6g
____ 0.6
= -6 ___ 0.6
g = -10
29. 32 = 5 - 3t ___ - 5 _______ - 5 27 = -3t
27 ___ -3
= -3t ____ -3
-9 = t
10 Holt McDougal Algebra 1
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30. 2d + 1 __ 5 = 3 __
5
______
- 1 __ 5
____ - 1 __
5
2d = 2 __ 5
1 __ 2 (2d) = 1 __
2 ( 2 __
5 )
d = 1 __ 5
31. 1 = 2x + 1 __ 2
- 1 __ 2
______ - 1 __
2
1 __ 2 = 2x
1 __ 2 ( 1 __
2 ) = 1 __
2 (2x)
1 __ 4 = x
32. z __ 2 + 1 = 3 __
2
_____ - 1 ___ - 1
z __ 2 = 1 __
2
2 ( z __ 2 ) = 2 ( 1 __
2 )
z = 1
33. 2 __ 3 =
4j __
6
( 6 __ 4 ) 2 __
3 = ( 6 __
4 ) 4 __
6 j
1 = j
34. 3 __ 4 = 3 __
8 x - 3 __
2
____
+ 2 __ 3
_______ + 3 __
2
9 __ 4 = 3 __
8 x
( 8 __ 3 ) 9 __
4 = ( 8 __
3 ) 3 __
8 x
6 = x
35. 1 __ 5 - x __
5 = - 2 __
5
________
- 1 __ 5
____ - 1 __
5
- x __ 5 = - 3 __
5
(-5) (- x __ 5 ) = (-5) (- 3 __
5 )
x = 3
36. 6 = -2(7 - c) 6 = (-2)(7) + (-2)(-c) 6 = -14 + 2c ____ + 14 _________ + 14 20 = 2c
20 ___ 2 = 2c ___
2
10 = c
37. 5(h - 4) = 8 (5)(h) + (5)(-4) = 8 5h - 20 = 8 _______ + 20 ____ + 20 5h = 28
5h ___ 5 = 28 ___
5
h = 28 ___ 5
38. -3x - 8 + 4x = 17 -3x + 4x - 8 = 17 x - 8 = 17 _____ + 8 ___ + 8 x = 25
39. 4x + 6x = 30 10x = 30
10x ____ 10
= 30 ___ 10
x = 3
40. 2(x + 3) = 10 (2)(x) + (2)(3) = 10 2x + 6 = 10 ______ - 6 ___ -6 2x = 4
2x ___ 2 = 4 __
2
x = 2
41. 17 = 3(p - 5) + 8 17 = (3)(p) + (3)(-5) + 8 17 = 3p - 15 + 8 17 = 3p - 7 ___ +7 ______ + 7 24 = 3p
24 ___ 3 =
3p ___
3
8 = p
42. Let w represent the number of weeks. 245 = 125 + 15w _____ - 125 ___________ - 125 120 = 15w
120 ____ 15
= 15w ____ 15
8 = w Jennifer needs to save for another 8 weeks to buy
the bike.
43. 2x + 13 = 17 ______ - 13 ____ - 13 2x = 4
2x ___ 2 = 4 __
2
x = 2
3x + 1 = 3(2) + 1 = 6 + 1 = 7
44. -(x - 1) = 5 (-1)(x)+(-1)(-1) = 5 -x + 1 = 5 ______ - 1 ___ - 1 -x = 4 (-1)(-x) = (-1)(4) x = -4 -4x = -4(-4) = 16
45. 5(y+10) = 40 (5)(y) + (5)(10) = 40 5y + 50 = 40 _______ - 50 ____ - 50 5y = -10
5y
___ 5 = -10 ____
5
y = -2
1 __ 4 y
= 1 __ 4 (-2)
= - 1 __ 2
46. 9 - 6x = 45 ________ - 9 ___ - 9 -6x = 36
-6x ____ -6
= 36 ___ -6
x = -6
x - 4 = -6 - 4 = -10
47. (2x + 7) + 30 + 63 = 180 2x + 100 = 180 ________ - 100 _____ - 100 2x = 80
2x ___ 2 = 80 ___
2
x = 40
11 Holt McDougal Algebra 1
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48. x + x + 115 = 180 2x + 115 = 180 ________ - 115 _____ - 115 2x = 65
2x ___ 2 = 65 ___
2
x = 32.5
49. (4x - 80) + 60 + 60 = 180 4x + 40 = 180 _______ - 40 - 40 4x = 140
4x ___ 4 = 140 ____
4
x = 35
50. 2n - 7 = 19 ______ + 7 ___ + 7 2n = 26
2n ___ 2 = 26 ___
2
n = 13
51. 8 - 3n = 2 - 8 - 8 -3n = -6
-3n ____ -3
= -6 ___ -3
n = 2
52. 2n + 5 = 11 ______ - 5 ___ - 5 2n = 6
2n ___ 2 = 6 __
2
n = 3
53a. Let s represent the number of years in a score. 1963 - 5s = 1863 ___________ - 1963 ______ - 1963 -5s = -100
-5s ____ -5
= -100 _____ -5
s = 20 There are 20 years in a score.
b. Let n repesent the number of scores. ns = 60 n(20) = 60
20n ____ 20
= 60 ___ 20
n = 3 There are 3 scores in 60 years.
54. 3t + 44 = 50 ______ - 44 ____ - 44 3t = 6
3t __ 3 = 6 __
3
t = 2
55. 3(x - 2) = 18 (3)(x) + (3)(-2) = 18 3x - 6 = 18 ______ + 6 ___ + 6 3x = 24
3x ___ 3 = 24 ___
3
x = 8
56. 15 = c __ 3 - 2
___ + 2 _____ + 2
17 = c __ 3
3(17) = 3 ( c __ 3 )
51 = c
57. 2x + 6.5 = 15.5 _______ - 6.5 _____ - 6.5 2x = 9
2x ___ 2 = 9 __
2
x = 4.5
58. 3.9w - 17.9 = -2.3 __________ + 17.9 ______ + 17.9 3.9w = 15.6
3.9w ____ 3.9
= 15.6 ____ 3.9
w = 4
59. 17 = x - 3(x + 1) 17 = x + (-3)(x) + (-3)(1) 17 = x - 3x - 3 17 = -2x - 3 ___ + 3 _______ + 3 20 = -2x
20 ___ -2
= -2x ____ -2
-10 = x
60. 5x + 9 = 39 _____ - 9 ___ - 9 5x = 30
5x ___ 5 = 30 ___
5
x = 6
61. 15 + 5.5m = 70 ___________ - 15 ____ - 15 5.5m = 55
5.5m _____ 5.5
= 55 ___ 5.5
m = 10
62. Let k represent the height of a kiwi. 4k + 20 = 108 ______ - 20 ____ - 20 4k = 88
4k ___ 4 = 88 ___
4
k = 22 A kiwi is 22 in. tall.
Possible answer: The height of an ostrich will be more than 4 times the height of a kiwi. 108 is more than 4(22) = 88, so 22 in. is reasonable.
63. Let k represent the height of a kakapo. 5k - 70 = 60 ______ + 70 ____ + 70 5k = 130
5k ___ 5 = 130 ____
5
k = 26 A kakapo is 26 in. tall.
Possible answer: The height of a kakapo will be more than 1 __
5 the height of an emu. 26 is more
than 1 __ 5 (60) = 12, so it is a reasonable answer.
64. Let n represent the first number. (n) + (n + 1) = 57 2n + 1 = 57 ______ - 1 ___ - 1 2n = 56
2n ___ 2 = 56 ___
2
n = 28 The numbers are n = 28 and n + 1 = 29.
12 Holt McDougal Algebra 1
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65. Let n represent Stan’s age. (n) + (n + 1) + (n + 2) = 111 3n + 3 = 111 ______ - 3 ___ - 3 3n = 108
3n ___ 3 = 108 ____
3
n = 36 Stan is n = 36, Mark is n + 1 = 37, and Wayne is n + 2 = 38.
66. Let n represent the first number. (n) + (n + 2) = 206 2n + 2 = 206 ______ - 2 ___ - 2 2n = 204
2n ___ 2 = 204 ____
2
n = 102 The numbers are n = 102 and n + 2 =104.
67a. Cost of Fighting Fire
Acres Cost ($)
100 22,500
200 45,000
500 112,500
1000 225,000
1500 337,500
n 225n
b. c = 225n
68. Possible answer: Distribute 2 or subtract 3 from both sides.
69. Possible answer: Simplify both sides if necessary. Find the term containing the variable. Undo any addition or subtraction on this term by using inverse operations. Then undo any multiplication or division on this term by using inverse operations.
teSt prep
70. D; g represents the number of shirts Greg sold. Lin sold g + 4 and Fran sold 3(g + 4) = 3g + 12. Therefore, the total number of shirts sold is
g + g + 4 + 3g + 12 = 16 + 5g, so D is correct.
71. H; Solving for m reveals m = 6, so 7m - 5 is 42 - 5 = 37.
72. C; Since m is multiplied by 0.06, there is a cost of $0.06 for each mile. Since 48 is added to 0.06m, there is an additional fee of $48. Therefore C is correct.
73. 27 sales 150 + 2s = 204 __________ - 150 _____ - 150 2s = 54
2s ___ 2 = 54 ___
2
s = 27
challenge and extend
74. 9 __ 2 x + 18 + 3x = 11 ___
2
9 __ 2 x + 3x + 18 = 11 ___
2
15 ___ 2 x + 18 = 11 ___
2
________ - 18 ____ - 18
15 ___ 2 x = - 25 ___
2
( 2 ___ 15
) ( 15 ___ 2 x) = ( 2 ___
15 ) (- 25 ___
2 )
x = - 5 __ 3
75. 15 ___ 4 x - 15 = 33 ___
4
________ + 15 ____ + 15
15 ___ 4 x = 93 ___
4
( 4 ___ 15
) 15 ___ 4 x = ( 4 ___
15 ) 93 ___
4
x = 6 1 __ 5
76. (x + 6) - (2x + 7) - 3x = -9 x + 6 + (-1)(2x) + (-1)(7) - 3x = -9 x + 6 -2x -7 - 3x = -9 x - 2x - 3x + 6 - 7 = -9 -4x - 1 = -9 _______ + 1 ___ + 1 -4x = -8
-4x ____ -4
= -8 ___ -4
x = 2
77. (4x + 2) - (12x + 8) + 2(5x - 3) = 6 + 11 4x + 2 - 12x - 8 + 10x - 6 = 6 + 11 4x - 12x + 10x + 2 - 8 - 6 = 6 + 11 2x - 12 = 17 _______ + 12 ____ + 12 2x = 29
2x ___ 2
= 29 ___ 2
x = 14.5
78. 4x + 3b = -1 4(2) + 3b = -1 8 + 3b = -1 ________ - 8 ___ - 8 3b = -9
3b ___ 3 = -9 ___
3
b = -3
79. 2x - 3b = 0 2(-9) - 3b = 0 -18 - 3b = 0 ________ +18 ____ + 18 -3b = 18
-3b ____ -3
= 18 ___ -3
b = -6
80a. p = nc - e 2500 = 2000c - 800 _____ + 800 ___________ + 800 3300 = 2000c
3300 _____ 2000
= 2000c ______ 2000
1.65 = c
b. p = nc - e 2500 = 1000c - 800 _____ + 800 ___________ + 800 3300 = 1000c
3300 _____ 1000
= 1000c ______ 1000
3.3 = c
c. c doubles
13 Holt McDougal Algebra 1
CS10_A1_MESK710372_C01.indd 13 3/30/11 10:30:58 PM
solVing equAtions with VAriAbles on both sides
CheCk it OUt!
1a. 4b + 2 = 3b ________ - 3b ____ - 3b b + 2 = 0 _____ - 2 ___ - 2 b = -2
b. 0.5 + 0.3y = 0.7y - 0.3 _________ - 0.3y ___________ - 0.3y 0.5 = 0.4y - 0.3 _____ + 0.3 _________ + 0.3 0.8 = 0.4y
0.8 ___ 0.4
= 0.4y
____ 0.4
2 = y
2a. 1 __ 2 (b + 6) = 3 __
2 b - 1
1 __ 2 (b) + 1 __
2 (6) = 3 __
2 b - 1
1 __ 2 b + 3 = 3 __
2 b - 1
________
- 1 __ 2 b
________ - 1 __
2 b
3 = b - 1 ___ + 1 _____ + 1 4 = b
b. 3x + 15 - 9 = 2(x + 2) 3x + 15 - 9 = 2(x) + 2(2) 3x + 15 - 9 = 2x + 4 3x + 6 = 2x + 4 ________ - 2x ________ - 2x x + 6 = 4 _____ - 6 ___ - 6 x = -2
3a. 4y + 7 - y = 10 + 3y 7 + 3y = 10 + 3y ______ - 3y _______ - 3y 7 = 10 7 no solution
b. 2c + 7 + c = -14 + 3c + 21 3c + 7 = 3c + 7 ________ - 3c ________ - 3c 7 = 7 3 all real numbers
4. Let g represent Greg’s age. 4g - 3 = 3g + 7 ________ - 3g ________ - 3g g - 3 = 7 _____ + 3 ___ + 3 g = 10 Greg is 10 years old.
think and disCUss
1. Equation b, 8.3x - 9 + 0.7x = 2 + 9x - 11 is an identity. The equation simplifies to 9x - 9 = 9x - 9 which is true for all values of x.
2. An equation with variables on both sides can have…
One solution: 5x - 4 = 4x + 5
Many solutions: 5x - 4 = 5x - 4
No solution: 5x - 4 = 5x - 3
eXeRCisesguided practice
1. Possible answer: After simplifying, the expressions on either side of the equal sign are the same.
2. 2c - 5 = c + 4 _______ - c _______ - c c - 5 = 4 _____ + 5 ___ + 5 c = 9
3. 8r + 4 = 10 + 2r ________ - 2r ______ - 2r 6r + 4 = 10 _____ - 4 ___ - 4 6r = 6
6r __ 6 = 6 __
6
r = 1
4. 2x - 1 = x + 11 _______ - x ________ - x x - 1 = 11 _____ + 1 ___ + 1 x = 12
5. 28 - 0.3y = 0.7y - 12 ________ + 0.3y __________ + 0.3y 28 = y - 12 ____ + 12 ______ + 12 40 = y
6. -2(x + 3) = 4x - 3 -2(x) - 2(3) = 4x - 3 -2x - 6 = 4x - 3 ________ + 2x ________ + 2x -6 = 6x - 3 ___ + 3 ______ + 3 -3 = 6x
-3 ___ 6 = 6x ___
6
- 1 __ 2 = x
7. 3c - 4c + 1 = 5c + 2 + 3 -c + 1 = 5c + 5 _______ + c _______ + c 1 = 6c + 5 ___ - 5 ______ - 5 -4 = 6c
-4 ___ 6 = 6c ___
6
- 2 __ 3 = c
8. 5 + 3(q - 4) = 2(q + 1) 5 + 3(q) + 3(-4) = 2(q) + 2(1) 5 + 3q -12 = 2q + 2 3q - 7 = 2q + 2 ________ - 2q ________ - 2q q - 7 = 2 _____ + 7 ___ + 7 q = 9
14 Holt McDougal Algebra 1
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9. 5 - (t + 3) = -1 + 2(t - 3) 5 - (t) - (3) = -1 + 2(t) + 2(-3) 5 - t - 3 = -1 + 2t - 6 2 - t = 2t - 7 ____ + t ______ + t 2 = 3t - 7 ___ + 7 _____ + 7 9 = 3t
9 __ 3 = 3t __
3
3 = t
10. 7x - 4 = -2x + 1 + 9x - 5 7x - 4 = 7x - 4 ________ - 7x _______ -7x -4 = -4 3 all real numbers
11. 8x + 6 - 9x = 2 - x - 15 6 - x = -13 - x _____ + x _______ + x 6 = -13 7 no solution
12. 6y = 8 - 9 + 6y 6y = -1 + 6y ____ - 6y _______ - 6y 0 = -1 7 no solution
13. 6 - 2x - 1 = 4x + 8 - 6x - 3 5 - 2x = 5 - 2x ______ + 2x ______ + 2x 5 = 5 3 all real numbers
14a. Let x represent the number of hours. 376 + 12x = 280 + 15x _________ - 12x _________ - 12x 376 = 280 + 3x _____ - 280 ___________ - 280 96 = 3x
96 ___ 3 = 3x ___
3
32 = x The two companies cost the same amount for a
32-hour job.
b. 376 + 12x = 376 + 12(32) = 376 + 384 = $760
practice and problem Solving
15. 7a - 17 = 4a + 1 _________ - 4a ________ - 4a 3a - 17 = 1 _______ + 17 ____ + 17 3a = 18
3a ___ 3 = 18 ___
3
a = 6
16. 2b - 5 = 8b + 1 ________ - 2b ________ - 2b -5 = 6b + 1 ___ - 1 ______ - 1 -6 = 6b
-6 ___ 6 = 6b ___
6
-1 = b
17. 4x - 2 = 3x + 4 ________ - 3x ________ - 3x x - 2 = 4 _____ + 2 ___ + 2 x = 6
18. 2x - 5 = 4x - 1 ________ - 2x ________ - 2x -5 = 2x - 1 ___ + 1 ______ + 1 -4 = 2x
-4 ___ 2
= 2x ___ 2
-2 = x
19. 8x - 2 = 3x + 12.25 ________ - 3x ___________ - 3x 5x - 2 = 12.25 ______ + 2 ______ + 2 5x = 14.25
5x ___ 5 = 14.25 _____
5
x = 2.85
20. 5x + 2 = 3x ________ - 5x ____ - 5x 2 = -2x
2 ___ -2
= -2x ____ -2
-1 = x
21. 3c - 5 = 2c + 5 ________ - 2c ________ - 2c c - 5 = 5 _____ + 5 ___ + 5 c = 10
22. -17 - 2x = 6 - x ________ + 2x ______ + 2x -17 = 6 + x ____ - 6 ________ - 6 -23 = x
23. 3(t - 1) = 9 + t 3(t) + 3(-1) = 9 + t 3t - 3 = 9 + t ______ - t _____ - t 2t - 3 = 9 _____ + 3 ___ + 3 2t = 12
2t __ 2
= 12 ___ 2
t = 6
24. 5 - x - 2 = 3 + 4x + 5 3 - x = 4x + 8 _____ + x _______ + x 3 = 5x + 8 ___ - 8 ______ - 8 -5 = 5x
-5 ___ 5 = 5x ___
5
-1 = x
25. 2(x + 4) = 3(x - 2) 2(x) + 2(4) = 3(x) + 3( -2) 2x + 8 = 3x - 6 ________ - 2x ________ - 2x 8 = x - 6 ___ + 6 _____ + 6 14 = x
26. 3m - 10 = 2(4m - 5) 3m - 10 = 2(4m) + 2(-5) 3m - 10 = 8m - 10 _________ - 3m _________ - 3m -10 = 5m - 10 ____ + 10 _______ + 10 0 = 5m
0 __ 5 = 5m ___
5
0 = m
15 Holt McDougal Algebra 1
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27. 5 - (n - 4) = 3(n + 2) 5 - 1(n) - 1(-4) = 3(n) + 3(2) 5 - n + 4 = 3n + 6 9 - n = 3n + 6 _____ + n _______ + n 9 = 4n + 6 ___ - 6 ______ - 6 3 = 4n
3 __ 4 = 4n ___
4
3 __ 4 = n
28. 6(x + 7) - 20 = 6x 6(x) + 6(7) - 20 = 6x 6x + 42 - 20 = 6x 6x + 22 = 6x _________ - 6x - 6x 22 = 0 7 no solution
29. 8(x + 1) = 4x - 8 8(x) + 8(1) = 4x - 8 8x + 8 = 4x - 8 ________ - 4x ________ - 4x 4x + 8 = -8 ______ - 8 ____ - 8 4x = -16
4x ___ 4 = -16 ____
4
x = -4
30. x - 4 - 3x = -2x - 3 - 1 -2x - 4 = -2x - 4 ________ + 2x ________ + 2x -4 = -4 3 all real numbers
31. -2(x + 2) = -2x + 1 -2(x) - 2(2) = -2x + 1 -2x - 4 = -2x + 1 ________ + 2x ________ + 2x -4 = 1 7 no solution
32. 2(x + 4) - 5 = 2x + 3 2(x) + 2(4) - 5 = 2x + 3 2x + 8 - 5 = 2x + 3 2x + 3 = 2x + 3 ________ + 2x ________ + 2x 3 = 3 3 all real numbers
33a. Let w represent the number of weeks. 150 + 2w = 195 - w ________ + w _______ + w 150 + 3w = 195 __________ -150 _____ -150 3w = 45
3w ___ 3 = 45 ___
3
w = 15
Justin and Tyson will weigh the same amount in 15 weeks.
b. 195 - w = 195 - 15 = 180 lb
34. 3(x + 4) = 18 + x 3(x) + 3(4) = 18 + x 3x + 12 = 18 + x ________ - x ______ - x 2x + 12 = 18 _______ - 12 ____ - 12 2x = 6
2x ___ 2 = 6 __
2
x = 3
35. x - 30 = 14 - 3x _________ + 3x _______ + 3x 4x - 30 = 14 _______ + 30 ____ + 30 4x = 44
4x ___ 4 = 44 ___
4
x = 11
36. 2x - 2 = x + 64 _______ - x ________ - x x - 2 = 64 _____ + 2 ___ + 2 x = 66
37. 2x - 2 = 4x + 6 ________ - 2x ________ - 2x -2 = 2x + 6 ___ - 6 ______ - 6 -8 = 2x
-8 ___ 2 = 2x ___
2
-4 = x
38. 3x + 5 = 2x + 2 ________ - 2x ________ - 2x x + 5 = 2 _____ - 5 ___ -5 x = -3
39. 4x + 3 = 5x - 4 ________ - 4x ________ - 4x 3 = x - 4 ___ + 4 _____ + 4 7 = x
40. - 2 __ 5 p + 2 = 1 __
5 p + 11
________
+ 2 __ 5 p
_________ + 2 __
5 p
2 = 3 __ 5 p + 11
____ - 11 _______ - 11
-9 = 3 __ 5 p
( 5 __ 3 ) (-9) = ( 5 __
3 ) ( 3 __
5 p)
-15 = p
41. 5x + 24 = 2x + 15 _________ - 2x _________ - 2x 3x + 24 = 15 _______ - 24 ____ - 24 3x = -9
3x ___ 3 = -9 ___
3
x = -3
42. 5x - 10 = 14 - 3x _________ + 3x _______ + 3x 8x - 10 = 14 _______ + 10 ____ + 10 8x = 24
8x ___ 8 = 24 ___
8
x = 3
43. 12 - 6x = 10 - 5x _______ + 6x _______ + 6x 12 = 10 + x ____ - 10 _________ - 10 2 = x
44. 5x - 7 = -6x - 29 ________ + 6x _________ + 6x 11x - 7 = -29 ______ + 7 ____ + 7 11x = -22
11x ___ 11
= -22 ____ 11
x = -2
45. 1.8x + 2.8 = 2.5x + 2.1 ___________ - 1.8x ___________ - 1.8x 2.8 = 0.7x + 2.1 _____ - 2.1 _________ - 2.1 0.7 = 0.7x
0.7 ___ 0.7
= 0.7x ____ 0.7
1 = x
16 Holt McDougal Algebra 1
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46. 2.6x + 18 = 2.4x + 22 __________ - 2.4x __________ - 2.4x 0.2x + 18 = 22 ________ - 18 ____ - 18 0.2x = 4
0.2x ____ 0.2
= 4 ___ 0.2
x = 20
47. 1 - 3x = 2x + 8 ______ + 3x ________ + 3x 1 = 5x + 8 ___ - 8 ______ - 8 -7 = 5x
-7 ___ 5 = 5x ___
5
- 7 __ 5 = x
48. 1 __ 2 (8 - 6h) = h
1 __ 2 (8) + 1 __
2 (-6h) = h
4 - 3h = h ______ + 3h ____ + 3h 4 = 4h
4 __ 4 = 4h ___
4
1 = h
49. 3(x + 1) = 2x + 7 3(x) + 3(1) = 2x + 7 3x + 3 = 2x + 7 _______ - 2x _______ - 2x x + 3 = 7 _____ - 3 ___ - 3 x = 4
50. 9x - 8 + 4x = 7x + 16 13x - 8 = 7x + 16 ________ - 7x _________ - 7x 6x - 8 = 16 ______ + 8 ___ + 8 6x = 24
6x ___ 6 = 24 ___
6
x = 4
51. 3(2x - 1) + 5 = 6(x + 1) 3(2x) +3(-1) + 5 = 6(x) + 6(1) 6x - 3 + 5 = 6x + 6 6x + 2 = 6x + 6 2 = 6
There is no solution.
52a. Let m represent the number of miles. 40 + 15 + 0.25m = 45 + 0.35m 55 + 0.25m = 45 + 0.35m __________ - 0.25m __________ - 0.25m 55 = 45 + 0.10m ____ - 45 ____________ - 45 10 = 0.10m
10 ____ 0.10
= 0.10m ______ 0.10
100 = m
45 + 0.35m = 45 + 0.35(100) = 45 + 35 = $80 Both companies charge $80 for a 100-mile rental. Possible answer: For 100 mi, Rapid Rental Car
charges $40 + $15 + $25 = $80. Capital Cars charges $45 + $35 = $80.
b. Capital Cars; the cost would be less.
c. No; now Rapid Rental Car would be cheaper.
d. Less than 100 mi - use Capital Cars; more than 100 mi - use Rapid Rental Car.
53. 3(x + 3) = (x + 3) + (2x - 3) + x 3(x) + 3(3) = (x + 3) + (2x - 3) + x 3x + 9 = x + 3 + 2x - 3 + x 3x + 9 = 4x ________ - 3x ____ - 3x 9 = x
54a. 420 + 60(2) = 420 + 120 = 540 acres
Possible answer: The total acreage in the next 2 days will be about 100 more than 420, so 540 is reasonable.
b. 420 + 60d c. 80d
d. 420 + 60d = 80d _________ - 60d _____ - 60d 420 = 20d
420 ____ 20
= 20d ____ 20
21 days = d d represents the number of days it will take the
firefighters to put out the fire.
55. Possible answer: 2x + 6 = x + 5 + x
56a. 47x 56b. 65x
c. 47x + 1
d. 47x + 1 = 65x - 47x - 47x 1 = 18x
1 ___ 18
= 18x ____ 18
1 ___ 18
= x
The cheetah will have to run for 1 ___ 18
h or about
3 1 __ 3 min to catch the gazelle.
e. No; the cheetah can only maintain its top speed for about 0.003 h, or about 11 s.
57. Possible answer: Simplify both sides if necessary. Collect the variable terms on one side by using inverse operations. Then isolate the variable using inverse operations.
teSt prep
58. C; Lindsey’s monthly magazine costs $1.25 per issue so her total cost is 1.25m. Kenzie got her first two magazines free so she paid for m - 2 magazines. Since Kenzie’s magazines cost $1.50, her total cost is 1.50(m - 2). So when
1.25m = 1.50(m - 2), they will have paid the same amount.
59. F; The equation is 7x = 5x - 3. Solving gives x = -1.5, which is F.
60. B; 3 packs of markers plus $9.00 will be equal to the cost of 5 packs of markers so B is correct.
61. H; In 133 days, or 19 weeks, she will save an additional 20(19) = $380. So she will have 380 + 120 = $500.
17 Holt McDougal Algebra 1
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62. 4 -2(x - 1) + 5x = 2(2x - 1) -2(x) - 2(-1) + 5x = 2(2x) + 2(-1) -2x +2 + 5x = 4x - 2 3x + 2 = 4x - 2 ________ - 3x ________ - 3x 2 = x - 2 ___ + 2 _____ + 2 4 = x
challenge and extend
63. 4x + 2[4 - 2(x + 2)] = 2x - 4 4x + 2(4) + 2[-2(x + 2)] = 2x - 4 4x + 8 - 4(x + 2) = 2x - 4 4x + 8 - 4(x) - 4(2) = 2x - 4 4x + 8 - 4x - 8 = 2x - 4 0 = 2x - 4 ___ + 4 _____ + 4 4 = 2x
4 __ 2 = 2x ___
2
2 = x
64. x + 5 _____ 2 + x - 1 _____
2 = x - 1 _____
3
6 ( x + 5 _____ 2
+ x - 1 _____ 2 ) = 6 ( x - 1 _____
3 )
6 ( x + 5 _____ 2 ) + 6 ( x - 1 _____
2 ) = 6 ( x - 1 _____
3 )
3x + 15 + 3x - 3 = 2x - 2 6x + 12 = 2x - 2 _________ - 2x ________ - 2x 4x + 12 = -2 _______ - 12 ____ - 12 4x = -14
4x ___ 4 = -14 ____
4
x = - 7 __ 2
65. 2 __ 3 w - 1 __
4 = 2 __
3 (w - 1 __
4 )
2 __ 3 w - 1 __
4 = 2 __
3 (w) + 2 __
3 (- 1 __
4 )
2 __ 3 w - 1 __
4 = 2 __
3 w - 1 __
6
_________
- 2 __ 3 w
_________ - 2 __
3 w
- 1 __ 4 = - 1 __
6 7
no solution
66. -5 - 7 - 3f = -f -2(f + 6) -5 - 7 - 3f = -f - 2(f ) - 2(6) -5 - 7 - 3f = -f -2f -12 -12 - 3f = -3f - 12 ________ + 3f ________ + 3f -12 = -12 3 all real numbers
67. 2 __ 3 x + 1 __
2 = 3 __
5 x - 5 __
6
_________
- 3 __ 5 x
________ - 3 __
5 x
1 ___ 15
x + 1 __ 2 = - 5 __
6
________
- 1 __ 2
____ - 1 __
2
1 ___ 15
x = - 4 __ 3
(15) ( 1 ___ 15
x) = (15) (- 4 __ 3 )
x = -20
68. x - 1 __ 4 = x __
3 + 7 3 __
4
_________
- 1 __ 3 x
_________ - 1 __
3 x
2 __ 3 x - 1 __
4 = 7 3 __
4
_______
+ 1 __ 4
____ + 1 __
4
2 __ 3 x = 8
( 3 __ 2 ) ( 2 __
3 x) = ( 3 __
2 ) (8)
x = 12
69. Let n represent the first number. 2(n + 2) = 3n - 2 2(n) + 2(2) = 3n - 2 2n + 4 = 3n - 2 ________ - 2n ________ - 2n 4 = n - 2 ___ +2 _____ + 2 6 = n The numbers are n = 6, n + 1 = 7, and n + 2 = 8.
70. Let n represent the first number. 2n = 12 + n + 2 2n = 14 + n ___ -n ______ - n n = 14 The numbers are n = 14, n + 1 = 15, and
n + 2 = 16.
71. Let r represent the amount of money Rob originally had.
r - 0.80 + 0.38 = r __ 2 - 0.38 + 0.80
r - 0.42 = 1 __ 2 r + 0.42
__________
- 1 __ 2 r
__________ - 1 __
2 r
1 __ 2 r - 0.42 = 0.42
_________ + 0.42 ______ + 0.42
1 __ 2 r = 0.84
(2) ( 1 __ 2 r) = (2)(0.84)
r = 1.68
Rob originally had $1.68.
solVing For A VAriAble
CheCk it OUt!
1. d = rt
d __ r = rt __ r
d __ r = t
t = d __ r
t = 26.2 ____ 18
t ≈ 1.46
It would take Van Dyk 1.46 hours.
2. f = i - gt _____ + gt _____ + gt f + gt = i
18 Holt McDougal Algebra 1
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3a. 5 - b = 2t
5 - b _____ 2 = 2t __
2
5 - b _____ 2
= t
b. D = m __ V
(V)(D) = (V) ( m __ V
)
VD = m
VD ___ D
= m __ D
V = m __ D
think and disCUss
1. Possible answer: The formula d = rt is more useful
in the form d __ r = t when you need to determine the
time it takes to travel a certain distance at a certain speed.
2. Possible answer: Isolate w on the right side by subtracting 2ℓ from both sides and then dividing both sides by 2.
3.
P = 4s; s = P _ 4
Common Formulas
Subject
Physical science
Formula
Geometry (perimeter of a
Earth science
square is 4 times the side length)
F = ma; m =
K = C + 273; C = K - 273 (temperature in kelvins is Celsius temperature plus 273)
F _ a
F _ m
; a =
equals mass times acceleration)
(force
eXeRCisesguided practice
1. A literal equation contains more than one variable. A formula shows how to determine the value of one variable when you know the value(s) of one or more other variables. So a formula always contains more than one variable, making it a literal equation.
2a. a = 46c
a ___ 46
= 46c ____ 46
a ___ 46
= c
b. c = a ___ 46
c = 322 ____ 46
c = 7
The room would need 7 circuits.
3. V = ℓwh
V ___ ℓh
= ℓwh ____ ℓh
V ___ ℓh
= w
4. st + 3t = 6 _____ - 3t ____ - 3t st = 6 - 3t
st __ t = 6 - 3t _____
t
s = 6 - 3t _____ t
5. m - 4n = 8 ______ + 4n ____ + 4n m = 8 + 4n
6. f + 4 _____ g = 6
(g) ( f + 4 _____ g ) = (g)(6)
f + 4 = 6g _____ - 4 ___ - 4 f = 6g - 4
7. b + c = 10 ___ a
(a)(b + c) = (a) ( 10 ___ a )
a(b + c) = 10
a(b + c)
_______ (b + c)
= 10 ______
(b + c)
a = 10 _____ b + c
practice and problem Solving
8a. C = 2πr
C ___ 2π
= 2πr ___ 2π
C ___ 2π
= r
b. r = C ___ 2π
r = 15 ___ 2π
r = 7.5 ___ π in.
9. A = P + I ____ - P _______ - P A - P = I
10. -2 = 4r + s ____ - 4r ________ - 4r -2 - 4r = s
11. xy - 5 = k _____ + 5 ___ + 5 xy = k + 5
xy
__ y = k + 5 _____ y
x = k + 5 _____ y
12. m __ n = p - 6
(n) ( m __ n ) = (n)(p - 6)
m = n(p - 6)
m ______ (p - 6)
= n(p - 6)
_______ (p - 6)
m _____ p - 6
= n
13. x - 2 _____ y = z
(y) ( x - 2 _____ y ) = (y)(z)
x - 2 = yz
x - 2 _____ z = yz
__ z
x - 2 _____ z = y
14. S = 180n - 360 _____ + 360 __________ + 360 S + 360 = 180n
S + 360 _______ 180
= 180n _____ 180
S + 360 _______ 180
= n
15. x __ 5 - g = a
_____ + g ___ + g
x __ 5 = a + g
(5) ( x __ 5 ) = (5)(a + g)
x = 5(a + g)
16. A = 1 __ 2
bh
A = h __ 2
b
( 2 __ h ) (A) = ( 2 __
h ) ( h __
2 b)
2A ___ h
= b
17. y = mx + b ___ - b ______ - b y - b = mx
y - b
_____ m = mx ___ m
y - b
_____ m = x
18. a = 3n + 1 ___ - 1 ______ - 1 a - 1 = 3n
a - 1 _____ 3
= 3n ___ 3
a - 1 _____ 3
= n
19. PV = nRT
PV ___ nR
= nRT ____ nR
PV ___ nR
= T
20. T + M = R _____ - M ____ - M T = R - M
21. M = T - R ____ + R _____ + R M + R = T
22. PV = nRT
PV ___ nT
= nRT ____ nT
PV ___ nT
= R
19 Holt McDougal Algebra 1
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23. 2a + 2b = c _________ - 2a ____ - 2a 2b = c - 2a
2b ___ 2 = c - 2a ______
2
b = c - 2a ______ 2
24. 5p + 9c = p _________ - 5p ____ - 5p 9c = -4p
9c ___ 9 =
-4p ____
9
c = - 4p
___ 9
25. ax + r = 7 ________ - ax ____ - ax r = 7 - ax
26. 3x + 7y = 2 _________ - 3x ____ - 3x 7y = 2 - 3x
7y
___ 7 = 2 - 3x ______
7
y = 2 - 3x ______ 7
27. 4y + 3x = 5 _________ - 4y ____ - 4y 3x = 5 - 4y
3x ___ 3 =
5 - 4y ______
3
x = 5 - 4y
______ 3
28. y = 3x + 3b ____ - 3x _________ - 3x y - 3x = 3b
y - 3x
______ 3 = 3b ___
3
y - 3x
______ 3 = b
29a. Possible answer: t ≈ d ____ 500
b. Possible answer: t ≈ d ____ 500
= 1300 _____ 500
= 2.6
It takes about 2.6 h to fly 1300 mi.
c. Possible answer: t ≈ d ____ 500
(500)(t) ≈ (500) ( d ____ 500
)
500t ≈ d
d. Possible answer: d ≈ 500t = 500(8) = 4000 The airplane can fly about 4000 mi in 8 h.
30. Ei = 9r
Ei __ i = 9r __
i
E = 9r __ i
E = 9(5)
____ 18
E = 2.5
The pitcher’s ERA is 2.5.
31. t = -0.0035a + g ___ - g ____________ - g t - g = -0.0035a
t - g ________
-0.0035 = -0.0035a _________
-0.0035
t - g ________
-0.0035 = a
32. Possible answer: Use inverse operations to isolate the indicated variable on one side of the equation. You must be sure the variable is the only expression on one side of the equation and doesn’t appear on the other side.
33. Possible answer: The variable a appears in 2 terms. Use the Distributive Property to write a - ab as
a(1 - b), and then divide both sides by 1 - b.
34a. Days Acres
1 60
2 120
3 180
4 240
5 300
d 60d
b. A = 60d
c. Extinguishing the Wildfire
0 1 2 3 4 5 6
100
200
300
400
Days A
cres
(5, 300) (4, 240)
(3, 180) (2, 120)
(1, 60)
The graph is a line.
teSt prep
35. C; First, subtract 9 from both sides. Then divide both sides by 3. Simplyfing the fraction gives C.
36. J; To isolate the b variable on the left side, subtract 2a from both sides. Then, since b is multiplied by -5, divide both sides by -5 to undo the multiplication.
37. D; Since Anna knows the length, width, and volume of the box, she need to find the height and therefore needs to solve for h.
challenge and extend
38. 3.3x + r = 23.1 _______ - r ____ - r 3.3x = 23.1 - r
3.3x ____ 3.3
= 23.1 - r _______ 3.3
x = 23.1 - r _______ 3.3
39. 2 __ 5 a - 3 __
4 b = c
_______
+ 3 __ 4 b
_____ + 3 __
4 b
2 __ 5 a = c + 3 __
4 b
( 5 __ 2 ) ( 2 __
5 a) = ( 5 __
2 ) (c + 3 __
4 b)
a = 5 __ 2 (c + 3 __
4 b)
20 Holt McDougal Algebra 1
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40. 3 __ 5 x + 1.4y = 2 __
5
___________
- 3 __ 5 x
_____ - 3 __
5 x
1.4y = 2 __ 5 - 3 __
5 x
1.4y
____ 1.4
= 2 __ 5 - 3 __
5 x _______
1.4
y = 2 __ 5 - 3 __
5 x _______
1.4
41. t = d ____ 500
+ 1 __ 2
____
- 1 __ 2
________ - 1 __
2
t - 1 __ 2 = d ____
500
(500) (t - 1 __ 2 ) = (500) ( d ____
500 )
500t - 250 = d
42. s = 1 __ 2 g t 2
s = t 2 ___
2g
( 2 __ t 2
) (s) = ( 2 __ t 2
) ( t 2 ___
2g )
2s ___ t 2
= g
43. v 2 = u 2 + 2as ____ - u 2 __________ - u 2 v 2 - u 2 = 2as
v 2 - u 2 _______ 2a
= 2as ____ 2a
v 2 - u 2 _______ 2a
= s
44. y = mx + 6 ___ - 6 ______ - 6 y - 6 = mx
y - 6
_____ x = mx ___ x
y - 6
_____ x = m
If m = 0, y - 6 = 0. Therefore y = 6.
45. S = hwft ______ 35,000
( 35,000
______ hwf
) (S) = ( 35,000
______ hwf
) ( hwft ______ 35,000
)
35,000S
_______ hwf
= t
t = 35,000S
_______ hwf
t = 35,000(2370)
___________ 320(144)(15)
t ≈ 120 s
solVing Absolute-VAlue equAtions
CheCk it OUt!
1a. |x| - 3 = 4 _____ + 3 ___ +3 |x| = 7 Case 1 Case 2 x = 7 x = -7
check ___________ |x| - 3 = 4 ____________ |x| - 3 = 4 |7| - 3 4 |-7| - 3 4 7 - 3 4 7 - 3 4 4 4 3 4 4 3
1b. 8 = |x - 2.5| Case 1 8 = x - 2.5
_____ + 2.5 _______ + 2.5 10.5 = x
Case 2
-8 = x - 2.5 _____ + 2.5 _______ + 2.5 -5.5 = x
check ___________ 8 = ⎜x - 2.5⎟ ___________ 8 = ⎜x - 2.5⎟ 8 8 8
⎜10.5 - 2.5⎟ ⎜8⎟ 8 3
8 8 8
⎜-5.5 - 2.5⎟ ⎜-8⎟ 8 3
2a. 2 - |2x - 5| = 7 ____________ -2 ___ -2 -|2x - 5| = 5 (-1)(-|2x - 5|) = (-1)(5) |2x - 5| = -5 7
no solution
2b. -6 + |x - 4| = -6 ___________ +6 ___ +6 |x - 4| = 0 x - 4 = 0 _____ + 4 ___ +4 x = 4
3. First convert millimeters to meters: 180 mm = 0.18 m. Find two numbers that are 0.18 units away from 134 by using the equation ⎜x - 134⎟ = 0.18.Case 1 x - 134 = 0.18 _______ + 134 _____ + 134 x = 134.18
Case 2 x - 134 = -0.18 _______ + 134 _____ + 134 x = 133.82
The minimum height of the bridge is 133.82 m, and the maximum height is 134.18.
think and disCUss
1. Multiply both sides by 5; split into two cases and solve each one.
2.
no solutions:
no solution
one solution: two solutions:
An absolute-value equation can have…
�x + 1� = -1 �x + 1� = 0 -1
�x + 1� = 2 -3, 1
21 Holt McDougal Algebra 1
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eXeRCisesguided practice
1. |x| = 6 Case 1 Case 2 x = 6 x = -6
check ________ |x| = 6 _________ |x| = 6 |6| 6 |-6| 6 6 6 3 6 6 3
2. 9 = |x + 5| Case 1 Case 2 9 = x + 5 -9 = x + 5 ___ -5 _____ - 5 ___ -5 _____ - 5 4 = x -14 = x
check _________ 9 = |x + 5| ____________ 9 = |x + 5| 9 |4 + 5| 9 |-14 + 5| 9 |9| 9 |-9| 9 9 3 9 9 3
3. |3x| + 2 = 8 ______ - 2 ___ -2 |3x| = 6 Case 1 Case 2 3x = 6 3x = -6
3x ___ 3 = 6 __
3 3x ___
3 = -6 ___
3
x = 2 x = -2
check ___________ |3x| + 2 = 8 ______________ |3x| + 2 = 8 |3(2)| + 2 8 |3(-2)| + 2 8 |6| + 2 8 |-6| + 2 8 6 + 2 8 6 + 2 8 8 8 3 8 8 3
4. 2|x| = 18
2|x| ___ 2 = 18 ___
2
|x| = 9 Case 1 Case 2 x = 9 x = -9
check _________ 2|x| = 18 ____________ 2|x| = 18 2|9| 18 2|-9| 18 2(9) 18 2(9) 18 18 18 3 18 18 3
5. ⎜x + 1 __ 2 ⎟ = 1
Case 1
x + 1 __ 2 = 1
_____
- 1 __ 2
____ - 1 __
2
x = 1 __ 2
Case 2
x + 1 __ 2 = -1
_____
- 1 __ 2
____ - 1 __
2
x = - 3 __ 2
check
__________
⎜x + 1 __ 2 ⎟ = 1
____________ ⎜x + 1 __
2 ⎟ = 1
⎜ 1 __ 2 + 1 __
2 ⎟
⎜1⎟ 1
1
1 1 3
⎜ 3 __ 2 + 1 __
2 ⎟
⎜1⎟ 1
1
1 1 3
6. ⎜x - 3⎟ - 6 = 2 __________ + 6 ___ + 6 ⎜x - 3⎟ = 8
Case 1 x - 3 = 8 _____ + 3 ___ + 3 x = 11
Case 2 x - 3 = -8 _____ + 3 ___ + 3 x = -5
check ______________ ⎜x - 3⎟ - 6 = 2 ______________ ⎜x - 3⎟ - 6 = 2
⎜11 - 3⎟ - 6 ⎜8⎟ - 6 8 - 6 2
2 2 2 2 3
⎜-5 - 3⎟ - 6 ⎜8⎟ - 6 8 - 6 2
2 2 2 2 3
7. -8 = |x| 7 no solution
8. |x| = 0 x = 0
check ________ |x| = 0
|0| 0 0 0 3
9. |x + 4| = -7 7 no solution
10. 7 = |3x + 9| + 7
___ -7 __________ - 7 0 = |3x + 9| 0 = 3x + 9 ___ -9 ______ - 9 -9 = 3x
-9 ___ 3 = 3x ___
3
-3 = x
check _________________ 7 = |3x + 9| + 7 7 |3(-3) + 9| + 7 7 |-9 + 9| + 7 7 |0| + 7 7 0 + 7 7 7 3
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11. ⎜2.8 - x⎟ + 1.5 = 1.5 - 1.5 - 1.5 ⎜2.8 - x⎟ = 0 2.8 - x = 0 _____________ + x ___ + x 2.8 = xcheck
⎜2.8 - x⎟ + 1.5 = 1.5
⎜2.8 - 2.8⎟ + 1.5 0 + 1.5 1.5
1.5 1.5 1.5 3
12. 5|x + 7| + 14 = 8 ___________ - 14 ____ -14 5|x + 7| = -6
5|x + 7| _______ 5 = -6 ___
5
|x + 7| = - 6 __ 5 7
no solution
13. Let x represent the mile-marker number. |x - 207| = 2 Case 1 Case 2 x - 207 = 2 x - 207 = -2 ______ + 207 _____ +207 _______ + 207 _____ +207 x = 209 x = 205
The walkie-takie will reach between mile marker 205 and mile marker 209.
practice and problem Solving
14. ⎜x⎟ = 1 __ 5
Case 1
x = 1 __ 5
Case 2
x = - 1 __ 5
check
_______
x = 1 __ 5
________ x = - 1 __
5
⎜ 1 __ 5 ⎟
1 __ 5
1 __ 5
1 __ 5 3
⎜ 1 __ 5 ⎟
1 __ 5
1 __ 5
1 __ 5 3
15. |2x - 4| = 22 Case 1 Case 2 2x - 4 = 22 2x - 4 = -22 _____ + 4 ___ +4 ______ + 4 ____ +4 2x = 26 2x = -18
2x ___ 2 = 26 ___
2 2x ___
2 = -18 ____
2
x = 13 x = -9
check _______________ |2x - 4| = 22 _______________ |2x - 4| = 22 |2(13) - 4| 22 |2(-9) - 4| 22 |26 - 4| 22 |-18 - 4| 22 |22| 22 |-22| 22 22 22 3 22 22 3
16. 18 = 3|x - 1|
18 ___ 3 = 3|x - 1| _______
3
6 = |x - 1| Case 1 Case 2 6 = x - 1 -6 = x - 1 ___ +1 _____ + 1 ___ +1 _____ + 1 7 = x -5 = x
check ____________ 18 = 3|x - 1| _____________ 18 = 3|x - 1| 18 3|7 - 1| 18 3|-5 - 1| 18 3|6| 18 3|-6| 18 3(6) 18 3(6) 18 18 3 18 18 3
17. -2|x| = -4
-2|x| _____ -2
= -4 ___ -2
|x| = 2 Case 1 Case 2 x = 2 x = -2
check ___________ -2|x| = -4 _____________ -2|x| = -4 -2|2| -4 -2|-2| -4 -2(2) -4 -2(2) -4 -4 -4 3 -4 -4 3
18. 3|x| - 12 = 18 _______ + 12 ____ +12 3|x| = 30
3|x| ___ 3 = 30 ___
3
|x| = 10 Case 1 Case 2 x = 10 x = -10
check _______________ 3|x| - 12 = 18 _________________ 3|x| - 12 = 18 3|10| - 12 18 3|-10| - 12 18 3(10) - 12 18 3(10) - 12 18 30 - 12 18 30 - 12 18 18 18 3 18 18 3
19. |x - 42.04| = 23.24 Case 1 Case 2 x - 42.04 = 23.24 x - 42.04 = -23.24 ________ + 42.04 ______ +42.04 ________ + 42.04 ______ +42.04 x = 65.28 x = 18.8
check _____________________ |x - 42.04| = 23.24 _____________________ |x - 42.04| = 23.24 |65.28 - 42.04| 23.24 18.8 - 42.04| 23.24 |23.24| 23.24 |-23.24| 23.24 23.24 23.24 3 23.24 23.24 3
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20. ⎜ 2 __ 3 x - 2 __
3 ⎟ = 2 __
3
Case 1 Case 2
2 __ 3 x - 2 __
3 = 2 __
3 2 __
3 x - 2 __
3 = - 2 __
3
______
+ 2 __ 3
___ + 2 __
3
_______ + 2 __
3
___ + 2 __
3
2 __ 3 x = 4 __
3 2 __
3 x = 0
( 3 __ 2 ) 2 __
3 x = ( 3 __
2 ) 4 __
3 ( 3 __
2 ) 2 __
3 x = ( 3 __
2 ) 0
x = 2 x = 0
check
______________
⎜ 2 __ 3 x - 2 __
3 ⎟ = 2 __
3
_______________ ⎜ 2 __
3 x - 2 __
3 ⎟ = 2 __
3
⎜ 2 __ 3 (2) - 2 __
3 ⎟ 2 __
3 ⎜ 2 __
3 (0) - 2 __
3 ⎟ 2 __
3
⎜ 4 __ 3 - 2 __
3 ⎟ 2 __
3 ⎜0 - 2 __
3 ⎟ 2 __
3
⎜ 2 __ 3 ⎟ 2 __
3 ⎜- 2 __
3 ⎟ 2 __
3
2 __ 3 2 __
3 3 2 __
3 2 __
3 3
21. |3x + 1| = 13 Case 1 Case 2 3x + 1 = 13 3x + 1 = -13 _____ - 1 ___ -1 ______ - 1 ____ -1 3x = 12 3x = -14
3x ___ 3 = 12 ___
3 3x ___
3 = -14 ____
3
x = 4 x = - 14 ___ 3
check _____________ |3x + 1| = 13 |3(4) + 1| 13 |12 + 1| 13 |13| 13 13 13 3
_________________ |3x + 1| = 13
⎜3 (- 14 ___ 3 ) + 1⎟ 13
|-14 + 1| 13 |-13| 13 13 13 3
22. ⎜-2x + 3⎟ = 5.8Case 1 -2x + 3 = 5.8 _______ - 3 ___ - 3 -2x = 2.8
-2x ____ -2
= 2.8 ___ -2
x = -1.4
Case 2 -2x + 3 = -5.8 _______ - 3 ___ - 3 -2x = -8.8
-2x ____ -2
= -8.8 _____ -2
x = 4.4check
⎜-2x + 3⎟ = 5.8 ⎜-2x + 3⎟ = 5.8
⎜-2(-1.4) + 3⎟ ⎜2.8 + 3⎟ ⎜5.8⎟ 5.8
5.8 5.8 5.8 5.8 3
⎜-2(4.4) + 3⎟ ⎜-8.8 + 3⎟ ⎜-5.8⎟ 5.8
5.8 5.8 5.8 5.8 3
23. ⎜4x⎟ + 9 = 9 - 9 - 9 ⎜4x⎟ = 0 4x = 0
4x ___ 4 = 0 __
4
x = 0check ____________ ⎜4x⎟ + 9 = 9
⎜4(0)⎟ + 9 ⎜0⎟ + 9 0 + 9 9
9 9 9 9 3
24. 8 = 7 - |x| ___ -7 _______ -7 1 = -|x| (-1)(1) = (-1)(-|x|) - 1 = |x| 7 no solution
25. |x| + 6 = 12 - 6 |x| + 6 = 6 _____ - 6 ___ -6 |x| = 0 x = 0
check ______________ |x| + 6 = 12 - 6 |0| + 6 6 0 + 6 6 6 6 3
26. ⎜x - 3⎟ + 14 = 5 ___________ - 14 ____ - 14 ⎜x - 3⎟ = -9 7no solution
27. 0 = ⎜ 2 __ 3 - x⎟
0 = 2 __ 3 - x
___ + x ______ + x
x = 2 __ 3
check
__________
0 = ⎜ 2 __ 3 - x⎟
0
0 0
⎜ 2 __ 3 - 2 __
3 ⎟
⎜0⎟ 0 3
28. 3 + ⎜x - 1⎟ = 3 ____________ - 3 ___ - 3 ⎜x - 1⎟ = 0 x - 1 = 0 ____________ + 1 ___ + 1 x = 1check _____________ 3 + ⎜x - 1⎟ = 3 3 + ⎜1 - 1⎟ 3 + ⎜0⎟ 3 + 0 3
3 3 3 3 3
29. Let x represent the diameter of the valve. |x - 5| = 0.001 Case 1 Case 2 x - 5 = 0.001 x - 5 = -0.001 ____ + 5 ______ +5 _____ + 5 ______ +5 x = 5.001 x = 4.999
The value can be between 4.999 mm and 5.001 mm.
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30. |n - 3| = 5 Case 1 Case 2 n - 3 = 5 n - 3 = -5 _____ + 3 ___ +3 _____ + 3 ___ +3 n = 8 n = -2
6 4 2 8 0 -2 -4
31. |x - 7| = 2 Case 1 Case 2 x - 7 = 2 x - 7 = -2 ____ + 7 ___ +7 _____ + 7 ___ +7 x = 9 x = 5
5 6 8 7 9
32. Let x represent the diameter. ⎜x - 6.5⎟ = 0.04Case 1 x - 6.5 = 0.04 ______ + 6.5 _____ + 6.5 x = 6.54
Case 2 x - 6.5 = -0.04 ______ + 6.5 _____ + 6.5 x = 6.46
Maximum diameter is 6.54 mm; minimum diameter is 6.46 mm.
33. Let x represent the number of bricks. |x - 1500| = 0.05(1500) |x - 1500| = 75 Case 1 Case 2 x - 1500 = 75 x - 1500 = -75 _______ + 1500 ______ +1500 ________ + 1500 ______ +1500 x = 1575 x = 1425
The maximum number of bricks is 1575, and the minimum number of bricks is 1425.
34. ⎜ℓ - 65.1⎟ = 0.2Case 1 ℓ - 65.1 = 0.2 _______ + 65.1 ______ + 65.1 ℓ = 65.3
Case 2 ℓ - 65.1 = -0.2 _______ + 65.1 ______ + 65.1 ℓ = 64.9
No; acceptable range is from 64.9 in. to 65.3 in.
35. 3 - (-3)
________ 2 = 6 __
2 = 3
3 - 3 = 0 Equation is ⎜x - 0⎟ = 3 ⎜x⎟ = 3
36. 1 - (-1)
________ 2 = 2 __
2 = 1
1 - 1 = 0 Equation is ⎜x - 0⎟ = 1 ⎜x⎟ = 1
37. 5 - (-1)
________ 2 = 6 __
2 = 3
5 - 3 = 2 Equation is ⎜x - 2⎟ = 3
38. 2 - (-4)
________ 2 = 6 __
2 = 3
2 - 3 = -1 Equation is ⎜x - (-1)⎟ = 3 ⎜x + 1⎟ = 3
39. sometimes; if equation simplifies to an absolute value on one side and a positive number on the other
40. sometimes; if x is non-negative
41. always; if x is non-negative, ⎜x⎟ = x is non-negative, and if x is negative, ⎜x⎟ = -x, which is non-negative.
42. Let x represent the temperature of the freezer. |x - 2| = 2.5 Case 1 Case 2 x - 2 = 2.5 x - 2 = -2.5 ____ + 2 ____ +2 _____ + 2 _____ +2 x = 4.5 x = -0.5
The maximum temperature in the freezer is 4.5˚F, and the minimum temperature in the freezer is -0.5˚F.
43a. |t - 24| = 5
b. Case 1 Case 2 t - 24 = 5 t - 24 = -5 _____ + 24 ____ +24 _____ + 24 ____ +24 t = 29 t = 19
c. yes, if you change the left side so that the measured wind speed is being subtracted from t
d. The measurement is correct within 5 mi/h.
44a. ⎜r - 55⎟
b. ⎜r - 55⎟ = 45
c. Case 1 r - 55 = 45 ______ + 55 ____ +55 r = 100
Case 2 r - 55 = -45 ______ + 55 ____ + 55 r = 10
Least: 10 gal/min Greatest: 100 gal/min
45. Possible answer: No; when an absolute-value expression equals 0, there is only one equation to solve. When an absolute-value expression equals a negative number, there is no equation to solve.
46. No; no matter what value of a is chosen, there will always be two solutions: a + 1 and a - 1.
teSt prep
47. C; Maximum and mimimum weights are (65 + 3) kg and (65 - 3) kg, respectively.
48. J; one case is n + 1 = -2 _____ - 1 ___ - 1 n = -3
49. B; because 95 - 90 _______ 2 = 2.5 and 95 - 2.5 = 92.5
25 Holt McDougal Algebra 1
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challenge and extend
50. P = 2ℓ + 2w 100 = 2 ⎜2x - 4⎟ + 2x ________ - 2x _____________ - 2x 100 - 2x = 2 ⎜2x - 4⎟ Case 1 100 - 2x = 2(2x - 4) 100 - 2x = 2(2x) - 2(4) 100 - 2x = 4x - 8 _________ + 8 ______ + 8 108 - 2x = 4x ________ + 2x ____ + 2x 108 = 6x
108 ____ 6 = 6x ___
6
18 = x Case 2 -(100 - 2x) = 2(2x - 4) -100 - (-2x) = 2(2x) - 2(4) -100 + 2x = 4x - 8 ____________ + 8 _______ + 8 -92 + 2x = 4x ____________ - 2x ____ - 2x -92 = 2x
-92 ____ 2 = 2x ___
2
-46 = x The value of x is 18 in.; solutions to equation are 18 and -46, but since x represents length, the negative solution is not reasonable.
51. Div. Prop. of Eq.; Subtr. Prop. of Eq.; Div. Prop. of Eq.
52. ⎜x⎟ = ⎜x + 1⎟ Case 1 x ≥ 0 x = x + 1 ___ - x ______ - x 0 = 1 7 no solution
Case 2 x < 0 if x + 1 < 0, then -x = -(x + 1) no solution as in Case 1 if x + 1 ≥ 0, then -x = x + 1 ____ - x ______ - x -2x = 1
-2x ____ -2
= 1 ___ -2
x = - 1 __ 2
check ⎜x⎟ = ⎜x + 1⎟
⎜- 1 __ 2 ⎟
1 __ 2
1 ____ 2
⎜- 1 __ 2 + 1⎟
⎜ 1 __ 2 ⎟
1 __ 2 3
reAdY to go on? section A quiz
1 – 4. Possible answers given:
1. the sum of 4 and n; n increased by 4
2. the difference of m and 9; 9 less than m
3. g divided by 2; the quotient of g and 2
4. 4 times z; the product of 4 and z
5. x - 32 = -18 _____ + 3 _ 2 ____ + 32 x = 14
6. 1.1 = m - 0.9 _____ + 0.9 _______ + 0.9 2 = m
7. j + 4 = -17 ____ ____ - 4 ____ - 4 j = -21
8. 9 __ 8 = g + 1 __
2
____
- 1 __ 2
______ - 1 __
2
5 __ 8 = g
9. Let s represent the space used on Soledad’s hard drive.
313 + s = 400 _________ - 313 _____ - 313 s = 87 Soledad used 87 GB of hard drive space in the first
six months.
10. h __ 3 = -12
(3) ( h __ 3 ) = (3)(-12)
h = -36
11. -2.8 = w ___ -3
(-3)(-2.8) = (-3) ( w ___ -3
)
8.4 = w
12. 42 = 3c
42 ___ 3 = 3c ___
3
14 = c
13. -0.1b = 3.7
-0.1b ______ -0.1
= 3.7 _____ -0.1
b = -37
14. Let g represent the amount of the goal.
3 __ 5 g = 2400
( 5 __ 3 ) ( 3 __
5 g) = ( 5 __
3 ) (2400)
g = 4000
The fund-raising goal was $4000.
15. 2r + 20 = 200 ______ - 20 ____ - 20 2r = 180
2r __ 2 = 180 ____
2
r = 90
16. 3 __ 5 k + 5 = 7
______ - 5 ___ - 5
3 __ 5 k = 2
( 5 __ 3 ) ( 3 __
5 k) = ( 5 __
3 ) (2)
k = 10 ___ 3
17. 5n + 6 - 3n = -12 2n + 6 = -12 ______ - 6 ____ - 6 2n = -18
2n ___ 2 = -18 ____
2
n = -9
18. 4(x - 7) = 2 4(x) + 4(-7) = 2 4x - 28 = 2 _______ + 28 ____ + 28 4x = 30
4x ___ 4 = 30 ___
4
x = 7.5
26 Holt McDougal Algebra 1
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19. Let m represent the number of miles Carmen traveled.
2.10 + 0.80m = 11.70 _____________ - 2.10 ______ - 2.10 0.80m = 9.6
0.80m ______ 0.80
= 9.6 ____ 0.80
m = 12 Carmen traveled 12 miles.
20. 4x - 3 = 2x + 5 ________ - 2x ________ - 2x 2x - 3 = 5 ______ + 3 ___ + 3 2x = 8
2x ___ 2 = 8 __
2
x = 4
21. 3(2x - 5) = 2(3x - 2) 3(2x) + 3(-5) = 2(3x) + 2(-2) 6x - 15 = 6x - 4 _________ - 6x ________ - 6x -15 = -4 7 no solution
22. 2(2t - 3) = 6(t + 2) 2(2t) + 2(-3) = 6(t) + 6(2) 4t - 6 = 6t + 12 _______ - 4t ________ - 4t -6 = 2t + 12 ____ - 12 ______ - 12 -18 = 2t
-18 ____ 2 = 2t __
2
-9 = t
23. 7(x + 5) = -7(x + 5) 7(x) + 7(5) = -7(x) - 7(5) 7x + 35 = -7x - 35 _________ + 7x _________ + 7x 14x + 35 = -35 _______ - 35 ____ - 35 14x = -70
14x ____ 14
= -70 ____ 14
x = -5
24. 2x + 3y = 12 ______ - 3y ____ - 3y 2x = 12 - 3y
2x ___ 2 =
12 - 3y _______
2
x = 12 - 3y
_______ 2
x = 6 - 3 __ 2 y
25. x __ r = v
(r) ( x __ r ) = (r)(v)
x = rv
26. 5j + s = t - 2 _____ + 2 ____ + 2 5j + s + 2 = t
27. h + p = 3(k - 8)
h + p
_____ 3
=
3(k - 8) _______
3
h + p
_____ 3
= k - 8
_____ + 8 _____ + 8
h + p
_____ 3
+ 8 = k
28. ⎜r⎟ = 7
Case 1 Case 2
r = -7 r = 7 29. ⎜h + 4⎟ = 11
Case 1 Case 2
h + 4 = -11 h + 4 = -11
_____ -4 ___ -4 _____ -4 ___ -4
h = -15 h = 7
30. ⎜2x + 4⎟ = 0
2x + 4 = 0
______ -4 ___ -4
2x = -4
2x ___ 2 = -4 ___
2
x = -2
31. 16 = 7 ⎜p + 3⎟ + 30
____ -30 __________ -30
-14 = 7 ⎜p + 3⎟
-14 ____ 7 =
7 ⎜p + 3⎟ ________
7
-2 = ⎜p + 3⎟ no solution
rAtes, rAtios, And proportions
CheCk it OUt!
1. 18 ÷ 3 __ 2
= 18 × 2 __ 3
= 12
2. 52.50 ÷ 7 = $7.50/h
3. 56 mi _____ 4 h
· 5280 ft ______ mi
· h _______ 3600 s
= 20.5 ̶
3 ft/s ≈ 20.5 ft/s
Possible answe r: The cyclist travels about 60 mi in 4 h, or 15 mi/h. There are about 5000 ft in 1 mi, so this speed is equivalent to 15(5000) = 75,000 ft/h. There are about 4000 s in 1 h, so this is equivalent
to 75,000
______ 4000
≈ 20 ft/s. So 20.5 ft/s is reasonable.
27 Holt McDougal Algebra 1
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CS10_A1_MESK710372_C01.indd 27 3/30/11 10:31:23 PM
4a. -5 ___ 2 =
y __
8
y = - 5 __ 2 × 8
y = -20
4b. g + 3
______ 5
= 7 __ 4
g + 3 = 7 __ 4 × 5
g = 35 ___ 4 - 12 ___
4
g = 23 ___ 4 = 5.75
5. 16 ___ x = 32 ___ 1
x = 16 ___ 32
x = 0.5 ft = 6 in.
think and disCUss
1. Possible answer: by using cross products; by multiplying both sides by 4 to isolate t.
2. Possible answer: 1 in. on the map represents 18 mi. So 0.625 in. will represent a little more than half of 18 mi. So 11.25 is reasonable.
3. Possible answers: rate: to compare quantities with different units; unit rate: to compare prices of products of different sizes; proportion: to solve for a missing quantity; conversion factor: to convert from one set of units to another.
Uses of Ratios
Proportion: to solve for a missing quantity
Unit rate: to compare prices of products of different sizes
Conversion factor: to convert from one set of units to another
Scale: to make scale drawings/models or to read distances from a map
Rate: to compare quantities with different units
eXeRCisesguided practice
1. The ratios are equivalent.
2. x ____ $64
= 3 __ 4
x = 3 __ 4 × $64
x = $48
3. x _________ 341 trillion
= 2 __ 1
x = 2 __ 1 × 341 trillion
= 682 trillion
4. x __ 1 = 2000 _____
40
x = 50 rotations/s
5. x __ 1 =
224,988 _______
12
x = 18,749 lb/cow
6. x __ 1 = 4.5 ___
9
x = 0.5 m/s
7. 4 1 __ 2 /h · 1 h ______
60 min
= 0.075 page/min
8. 18 ft ____ 2 s
· 3600 s ______ 1 h
· 1 mi ______ 5280 ft
≈ 6.14 mi/h
9. 125 yards
___________ 1 tablespoon
· 256 tablespoons
______________ 1 gallon
· 1 mi __________ 1760 yards
= 18 mi/gal
10. 3 __ z = 1 __ 8
1(z) = 3(8) z = 24
11. x __ 3 = 1 __
5
5(x) = 1(3) 5x = 3
x = 3 __ 5
12. b __ 4 = 3 __
2
2(b) = 4(3) 2b = 12 b = 6
13. f + 3 _____ 12
= 7 __ 2
2(f + 3) = 12(7) 2f + 6 = 84 ____ - 6 ___ - 6 2f = 78 f = 39
14. -1 ___ 5 = 3 ___
2d
-1(2d) = 5(3) -2d = 15 d = -7.5
15. 3 ___ 14
= s - 2 _____ 21
14(s - 2) = 21(3)14s - 28 = 63 _______ + 28 ____ + 28 14s = 91 s = 6.5
16. -4 ___ 9 = 7 __ x
-4(x) = 7(9) -4x = 63 x = -15.75
17. 3 _____ s - 2
= 1 __ 7
1(s - 2) = 3(7) s - 2 = 21 _____ + 2 ____ + 2 s = 23
18. 10 ___ h = 52 ___
13
52(h) = 10(13) 52h = 130 h = 2.5
19. Let h be the height of the Altar Stone.
3 __ 5 = h ___
4.9
5(h) = 4.9(3) 5h = 14.7 h = 2.94 m
practice and problem Solving
20. 6 __ x = 1 __ 9
1(x) = 6(9) x = 54 in.
21. x ______ 12,000
= 3 ____ 500
500(x) = 12,000(3) 500x = 36,000 x = 72
22. 25 lb _____ 4 gal
= 6.25 lb/gal
23. $6058.50
________ 15 oz
= $403.90/oz
24. 11.9 ft ______ 3 days
= 11.9 ft ______ 3 days
· 1 day
_____ 24 h
· 12 in. _____ 1 ft
≈ 1.98 in./h11.9 ft in 3 days is roughly equivalent to 12 ft
in 72 h, or 12 ___ 72
= 1 __ 6 ft/h. There are 12 in.
in 1 ft, so this speed is equivalent to 12 ___ 6 = 2 in./h.
So 1.98 in./h is reasonable.
28 Holt McDougal Algebra 1
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25. 694 m/s
= 694 m ______ 1 s
· 3600 s ______ 1 h
· 1 km _______ 1000 m
= 2498.4 km/h
26. v __ 6 = 1 __
2
2(v) = 6(1)
2v ___ 2 = 6 __
2
v = 3
27. 2 __ 5 = 4 __ y
2(y) = 4(5)
2y
___ 2 = 20 ___
2
y = 10
28. 2 __ h = -5 ___
6
(-5)(h) = 2(6)
(-5)h
_____ (-5)
= 12 ____
(-5)
h = -2.4
29. 3 ___ 10
= b + 7 _____ 20
10(b + 7) = 20(3) 10b + 70 = 60 _______ - 70 ____ - 70 10b = -10
10b ____ 10
= -10 ____ 10
b = -1
30. 5t __ 9 = 1 __
2
2(5t) = 1(9)
10t ___ 10
= 9 ___ 10
t = 0.9
31. 2 __ 3 = 6 _____
q - 4
2(q - 4) = 3(6) 2q - 8 = 18 _____ + 8 ____ + 8 2q = 26
2q
___ 2 = 26 ___
2
q = 13
32. x __ 8 = 7.5 ___
20
20(x) = 8(7.5)
20x ____ 20
= 60 ___ 20
x = 3
33. 3 __ k = 45 ___
18
45(k) = 3(18)
45k ____ 45
= 54 ___ 45
k = 1.2
34. 6 __ a = 15 ___ 17
15(a) = 6(17)
15a ____ 15
= 102 ____ 15
a = 6.8
35. 9 __ 2 = 5 _____
x + 1
9(x + 1) = 2(5) 9x + 9 = 10 ______ - 9 ___ - 9 9x = 1
9x ___ 9 = 1 __
9
x = 1 __ 9
36. 3 __ 5 = x ____
100
5(x) = 3(100)
5x ___ 5 = 300 ____
5
x = 60
37. 38 ___ 19
= n - 5 _____ 20
19(n - 5) = 20(38) 19n - 95 = 760 ______ + 95 ____ + 95 19n = 855
19n ____ 19
= 855 ____ 19
n = 45
38. 100 ____ 1 = 30 mm ______ x
100x = 30 mm x = 0.3 mmSo, the dust mite is 0.3 mm long.
39. x ___ 70
= 60 ___ 50
50(x) = 60(70)
50x ____ 50
= 4200 _____ 50
x = $8470 euro will be worth more than $60, so $84 is reasonable.
40. 20 ___ 85
= 100 ____ c
20(c) = 100(85)
20c ____ 20
= 8500 _____ 20
c = 425 carp
41. Possible answer: The denominator in the first ratio is the number of varsity members, but in the second ratio it is the total number of people on the team.
42a. v = d __ t
100 m ______ 10.5 s
≈ 9.52 m/s 200 m ______ 21.3 s
≈ 9.39 m/s
800 m ______ 113.3 s
≈ 7.06 m/s 5000 m _______ 864.7 s
≈ 5.78 m/s
b. The 100 m race has the fastest speed, whereas, the 5000 m race has the slowest speed.
c. Possible answer: Runners can maintain a very high speed for a short distance, but over a longer distance their speed drops.
43. 216 frames - 203 frames _____________________ 8 hours
= 1.625 frames/h
44. x - 1 _____ 3
= x + 1 _____ 5
5(x - 1) = 3(x + 1) 5x - 5 = 3x + 3 ________ - 3x + 5 ________ - 3x + 5 2x = 8
2x ___ 2 = 8 __
2
x = 4
45. m __ 3
= m + 4 ______ 7
7(m) = 3(m + 4) 7m = 3m + 12 _____ - 3m _________ - 3m 4m = 12
4m ___ 4
= 12 ___ 4
m = 3
46. 1 _____ x - 3
= 3 _____ x - 5
1(x - 5) = 3(x - 3) x - 5 = 3x - 9 ________ - 3x + 5 ________ - 3x + 5 -2x = -4
-2x ____ -2
= -4 ___ -2
x = 2
47. a __ 2
= a - 4 _____ 30
30(a) = 2(a - 4) 30a = 2a - 8 ____ - 2a ________ - 2a 28a = -8
28a ____ 28
= -8 ___ 28
a = - 2 __ 7
29 Holt McDougal Algebra 1
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48. 3 ___ 2y
= 16 _____ y + 2
3(y + 2) = 16(2y) 3y + 6 = 32y ________ - 3y ____ - 3y 6 = 29y
6 ___ 29
= 29y
____ 29
y = 6 ___ 29
49. n + 3 _____ 5
= n - 1 _____ 2
2(n+3) = 5(n - 1) 2n + 6 = 5n - 5 ________ - 5n - 6 ________ - 5n - 6 -3n = -11
-3n ____ -3
= -11 ____ -3
n = 11 ___ 3
50. 1 __ y = 1 ______ 6y - 1
1(6y - 1) = 1(y) 6y - 1 = y _______ - y + 1 _______ - y + 1 5y = 1
5y
___ 5
= 1 __ 5
y = 1 __ 5
51. 2 __ n = 4 _____ n + 3
2(n + 3) = 4(n) 2n + 6 = 4n ________ - 4n - 6 ________ - 4n - 6 -2n = -6
-2n ____ -2
= -6 ___ -2
n = 3
52. 5t - 3 ______ -2
= t + 3 _____ 2
2(5t - 3) = -2(t + 3) 10t - 6 = -2t - 6 _______ + 2t + 6 _______ + 2t + 6 12t = 0 t = 0
53. 3 _____ d + 3
= 4 ______ d + 12
3(d + 12) = 4(d + 3) 3d + 36 = 4d + 12 _________ - 4d - 36 _________ - 4d - 36 -d = -24
-d ___ -1
= -24 ____ -1
d = 24
54. 3x + 5 ______ 14
= x __ 3
3(3x + 5) = 14(x) 9x + 15 = 14x __________ - 14x - 15 __________ - 14x - 15 -5x = -15
-5x ____ -5
= -15 ____ -5
x = 3
55. 5 ___ 2n
= 8 _______ 3n - 24
5(3n - 24) = 8(2n) 15n - 120 = 16n ___________ - 16n + 120 ___________ - 16n + 120 -n = 120
-n ___ -1
= 120 ____ -1
n = -120
ApplicAtions oF proportions
CheCk it OUt!
1. 7 __ 5 = x __
2
5(x) = 7(2)
5x ___ 5 = 14 ___
5
x = 2.8 in.
2a. 150 ____ x = 45 ____ 195
45(x) = 150(195)
45x ____ 45
= 29,250
______ 45
x = 650 cm
b. 5.5 ___ x = 3.5 ___ 28
3.5(x) = 5.5(28)
3.5x ____ 3.5
= 154 ____ 3.5
x = 44 ft
3. The ratio of the perimeters is equal to the ratio of the corresponding sides.
think and disCUss
1. Possible answer: a model airplane and the real airplane it represents; a baseball and a softball; a photograph and its enlargement
2. �ABC ∼ �DEF
AB corresponds to DE. BC corresponds to EF. AC corresponds to DF.
Angle A corresponds to angle D. Angle B corresponds to angle E. Angle C corresponds to angle F.
Corresponding angles:
A
B E
D
FC
Corresponding sides:
eXeRCisesguided practice
1. They are the same shape but not necessarily the same size.
2. 5 ___ 4 = 7 __ x
5x = 28
5x ___ 5 = 28 ___
5
x = 5.6 m
3. 4 __ 8 = 5 __ x
4x = 40
4x ___ 4 = 40 ___
4
x = 10 ft
4. 5 __ h = 3.5 ___
14
3.5h = 70
3.5h ____ 3.5
= 70 ___ 3.5
h = 20 ft
5. The ratio of the areas is the square of the ratio of the corresponding side lengths.
practice and problem Solving
6. 2 __ 4 = 4 __ x
2x = 16
2x ___ 2 = 16 ___
2
x = 8 m
7. 2 ___ 10
= x ___ 35
10x = 70
10x ____ 10
= 70 ___ 10
x = 7 in.
8. 18 ____ h = 20 ___
42
20h = 756
20h ____ 20
= 756 ____ 20
h = 37.8 ft
9. The ratio of the perimeters is equal to the ratio of the corresponding side lengths.
30 Holt McDougal Algebra 1
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10. 2 1 __
2 ___
2 =
6 1 __ 4 ___ x
2 1 __ 2 x = 12 2 __
4
2 1 __
2 x ____
2 1 __ 2 =
12 2 __ 4 ____
2 1 __ 2
x = 5 ft
Possible answer: The width is less than the length for the baby blanket, so the width on the mother’s blanket will also be less than the length. Since 5 ft is
less than 6 1 __ 4 ft, 5 ft is a reasonable answer.
11. 120 ____ x = ( 1 __ 2 )
2
120 ____ x = 1 __ 4
x = 480 ft 2
12. 64 ___ 16
= ( x __ 1 )
2
64 ___ 16
= x 2 __ 1
x 2 = 4 x = 2
13. 6272 _____ 98
= ( x __ 1 )
3
64 = x 3 x = 4
14. 12 ___ x = 8 __ 6
8x = 72
8x ___ 8 = 72 ___
8
x = 9 m
15. 14 ___ x = 10 ___ 2
10x = 28
10x ____ 10
= 28 ___ 10
x = 2.8 ft
16. 7 ___ x = 8 ___ 10
8x = 70
8x ___ 8 = 70 ___
8
x = 8.75 ft
17. 8 __ x = 3 + 3 _____ 3
6x = 24
6x ___ 6 = 24 ___
6
x = 4 cm
18. 4 ___ x = 6 ____ 450
6x = 1800
6x ___ 6 = 1800 _____
6
x = 300 ft
19. Possible answer: No; a 16-in. pizza actually has 4 times the area, so the cost should be 4 times as much.
20a. 12 ____ 100
; 18 ____ 100
; 25 ____ 100
; 67 ____ 100
; 98 ____ 100
b. 0.12; 0.18; 0.25; 0.67; 0.98
c. The decimal is the percent with its decimal point moved two places to the left and the % symbol removed.
21. 1.5 ___ x = 4.5 ___ 36
4.5x = 54
4.5x ____ 4.5
= 54 ___ 4.5
x = 12 m
22. 40 ____ x = 30 ___ 72
30x = 2880
30x ____ 30
= 2880 _____ 30
x = 96 m
23. k 2
teSt prep
24. C; The radius of the first ball is twice the radius of the second. Since 2 3 = 8, to find the volume of the smaller sphere, divide 800 by 8.
25. G; Students can look at the first ratio in each similarity statement and check that the letters S and G are in the same position as M and W. Only choice G has them placed incorrectly.
26. 3 __ x = 5 ____ 7.25
5x = 21.75
5x ___ 5 = 21.75 _____
5
x = 4.35 cmchallenge and extend
27. 6 __ w = 4.5 ___ 3
4.5w = 18
4.5w ____ 4.5
= 18 ___ 4.5
w = 4 m
4 __ y = 3 __ 6
3y = 24
3y
___ 3 = 24 ___
3
y = 8 m
10 ___ x = 8 __ 6
8x = 60
8x ___ 8 = 60 ___
8
x = 7.5 m
28. b 2
29. Let A represent the area of rectangle B, w represent width, and P represent perimeter.
A ______ 30.195
= ( 2 __ 3 )
2
A ______ 30.195
= 4 __ 9
9A = 120.78
9A ___ 9 = 120.78 ______
9
A = 13.42 cm 2
A = ℓ · w
w = A ___ 6.1
w = 13.42 _____ 6.1
w = 2.2 cm
P = 2(ℓ + w)P = 2(6.1 + 2.2)P = 2(8.3)P = 16.6 cm
31 Holt McDougal Algebra 1
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precision And AccurAcY
CheCk it OUt! 1a. An ounce is a smaller than a pound, so 17 oz.
is more precise.
b. A hundredth of a meter is smaller than a tenth of a meter, so 7.85 m is more precise.
c. A gram is smaller than a kilogram, so 6000 g is more precise.
2a. Scales A and B measure to the nearest tenth of an ounce. Scale C measures to the nearest hundreth of ounce. Scale C is the most precise because a hundreth of an ounce is smaller than a tenth of an ounce.
b. Scale A: |16.00 - 16.3| = 0.3 Scale B: |16.00 - 15.8| = 0.2 Scale C: |16.00 - 16.07| = 0.07 Because 0.07 < 0.2 < 0.3, Scale C is the most
accurate. 3. 5.25 oz - 0.25 oz = 5.0 oz
5.25 oz + 0.25 oz = 5.50 ozThe lacrosse balls must be between 5.0 and 5.50 oz. Ball C does not fall between the specified tolerance because its weight is greater than the maximum weight of 5.50 oz.
4a. 4.1(0.05) = 0.21 4.1 in. ± 0.21 in. 3.89 in. - 4.31 in.
b. 475(0.025) = 11.88 475 m ± 11.88 m 463.12 m-486.88 m
c. 85(0.005) = 0.43 85 mg ± 0.43 mg 84.57 mg-85.43 mg
think and disCUss
1. Precision has to do with how small the units of measure are. Accuracy has to do with how close the measured quantity is to the actual quantity.
2. Possible answer: the length of a handmade candlestick
3. Measurement
Precision:weighingchemicalsin a lab
Accuracy:weightlimits on abridge
Tolerance:manufacturingnuts and bolts
eXeRCisesguided practice
1. The answer is precise because precision relates to the smallest unit that a ruler can measure.
2. The answer is accurate because accuracy relates to how close the scale can measure an object’s true mass.
3. 4.3 mLA tenth of a milliliter is smaller than a milliliter, so 4.3 mL is more precise.
4. 6.8 mA tenth of a meter is smaller than a meter, so 6.8 m is more precise.
5. 2.37 mgA hundredth of a milligram is smaller than a tenth of milligram, so 2.37 mg is the most precise.
6. 6.5 lbA tenth of a pound is smaller than a pound, so 6.5 lb is the most precise.
7. 47.3 ftA tenth of a foot is smaller than a foot, so 47.3 ft is more precise.
8. 13.9 ozA tenth of an ounce is smaller than an ounce, so 13.9 oz is more precise.
9a. Scale 1 measures to the nearest hundreth of a gram. Scales 2, 3, 4, and 5 measure to the nearest tenth of a gram. Scale 1 is the most precise because a hundreth of a gram is smaller than a tenth of a gram.
b. Scale 1: |10.00 - 9.98| = 0.02 Scale 2: |10.00 - 9.9| = 0.1 Scale 3: |10.00 - 10.1| = 0.1 Scale 4: |10.00 - 10.3| = 0.3 Scale 5: |10.00 - 9.8| = 0.2 Because 0.02 < 0.1 < 0.2 < 0.3, Scale 1 is the
most accurate.
10. Jen’s, Bill’s and Sasha’s odometers measure to the nearest hundreth of a mile. Rasheed’s odometer measures to the nearest thousandth of a mile. Rasheed’s odometer is the most precise because a thousandth of a mile is smaller than a hundredth of a mile.Jen: |1.000 - 1.01| = 0.01Bill: |1.000 - 0.97| = 0.03Rasheed: |1.000 - 0.989| = 0.011Sasha: |1.000 - 1.02| = 0.02Because 0.01 < 0.011 < 0.02 < 0.03, Jen’s odometer is the most accurate.
32 Holt McDougal Algebra 1
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11. 595.5 g - 28.5 g = 567.0 g595.5 g + 28.5 g = 624.0 gNo. Basketball 4 does not fall between the specified tolerance because 624.5 g is greater than the maximum allowable mass of 624.0 g.
12. 51.5 in. - 2.5 in. = 49.0 in.51.5 in. + 2.5 in. = 54.0 in.No; basketballs 3 and 4 do not fall between the specified tolerance because their bounce heights of 60.0 in. and 55.2 in. are greater than the maximum allowable bounce height, respectively.
13. 50(0.02) = 1.0050 lb ± 1.00 lb49.00 lb-51.00 lb
14. 100(0.005) = 0.5100 yd ± 0.5 yd99.5 yd-100.5 yd
15. 25(0.04) = 1.0025 cm ± 1.00 cm24.00 cm-26.00 cm
16. 400(0.06) = 24.00400 L ± 24.00376.00 L-424.00 L
17. 250(0.04) = 10.00250 mm ± 10.00 mm240.00 mm-260.00 mm
18. 70(0.03) = 2.1070 kg ± 2.1067.90 kg-72.10 kg
practice and problem Solving
19. One milligram is equal to one thousandth of a gram, so 4337 mg is the more precise measurement.
20. One inch is smaller than one foot, so 122 in. is more precise.
21. One lb is smaller than one ton, so 11,000 lb is more precise.
22. One cup is smaller than one pint, so 3 cups is more precise.
23. 6.83 cm equals 68.3 mm. A tenth of a millimeter is smaller than a millimeter, so 6.83 cm is more precise.
24. One tenth of a km is smaller than one mile, so 4.5 km is more precise.
25. 0.0127 m equals 1.27 cm. One hundredth of a centimeter is smaller than one centimeter, so 0.0127 m is more precise.
26. 115 oz equals 7.1875 lb. One ten thousandth of a pound is smaller than one hundreth of a pound, so 115 oz is more precise.
27a. Lucy’s cell phone measures time to the nearest tenth of a second. Juan and Pei’s cellphones measure time to the nearest hundredth of a second. Chandra’s cell phone measures time to the nearest thousandth of a second. Chandra’s cell phone is the most precise because a thousandth of a second is smaller than a hundredth of a second and a tenth of a second.
b. Lucy: |51.12 - 51.1| = 0.02 Juan: |51.12 - 52.23| = 0.11 Chandra: |51.12 - 51.769| = 0.649 Pei: |51.12 - 50.97| = 0.15 Because 0.02 < 0.11 < 0.15 < 0.649, Lucy’s
cell phone is the most accurate.
28. 100 in. + 0.25 in. = 100.25 in. 100 in. - 0.25 in. = 99.75 in.
100 5 __ 16
= 100.3125
Board 4’s length does not fall between the specified tolerance because 100.3125 in. is greater than the maximum allowable board length.
29. 45(0.02) = 0.9045 lb ± 0.90 lb44.10 lb-45.90 lb
30. 3(0.05) = 0.153 m ± 0.15 m2.85 m-3.15 m
31. 37(0.015) = 0.5637° C ± 0.56° C36.44° C-37.56° C
32. 750(0.03) = 22.50750 kg ± 22.50 kg727.50 kg-772.50 kg
33. 30(0.04) = 1.2030 ft ± 1.20 ft28.80 ft-31.20 ft
34. 550(0.08) = 44.00550 mL ± 44.00 mL506.00 mL-594.00 mL
35. 0.2(0.05) = 0.010.2 cm ± 0.01 cm0.19 cm-0.21 cm
36. 0.25(0.1) = 0.0250.25 kg ± 0.0250.23 kg-0.28 kg
37. 5456 mi
38. 3.63 m
39. 120 ft
40. 62.3 cg
41. 5,721 mg = 5.721 kg
5.721 kg equals 6 kg when rounded to the nearest kilogram.
33 Holt McDougal Algebra 1
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42. 0.4586 km = 458.6 m0.4586 km equals 459 m when rounded to the nearest meter.
43. 16.270 liters = 16,270 mLA tenth of a milliliter is smaller than a milliliter, so 16,453.2 mL is more precise.
44. 437 mm = 43.7 cm A tenth of a centimeter is smaller than a centimeter, so 437 mm is more precise.
45. 0.265 cm = 2.65 mmA hundredth of a millimeter is smaller than a millimeter, so 0.265 cm is more precise.
46. 5.20 kg = 5200 mgA tenth of a milligram is smaller than a milligram, so 5200.0 mg is more precise.
47. 55 yd = 165 ftOne foot is smaller than one yard, so 165 ft is more precise.
48. One tenth of an hour equals six minutes. One minute is smaller than one tenth of an hour, so 67 min is more precise
49. 33 mg = 0.033 g1 mg = 0.001 gOne milligram equals one thousandth of a gram, so the measurements have the same precision.
50. 42.7 cm = 427 mmA tenth of a millimeter is smaller than a millimeter, so 427.0 mm is more precise.
51. 0.475 L = 475 mLA tenth of a milliliter is smaller than a milliliter, so 475.0 mL is more precise.
52. ( 2 ____ 100
) · 100 = 2%
100 m ± 2%
53. ( 2 ___ 50
) · 100 = 4%
50 g ± 4%
54. ( 12 ____ 240
) · 100 = 5%
240 ft ± 5%
55. ( 15 ____ 750
) · 100 = 2%
750 kg ± 2%
56. ( 0.25 ____ 25
) · 100 = 1%
25 in. ± 1%
57. ( 8.5 ____ 425
) · 100 = 2%
425 lb ± 2%
58. ( 1.5 ___ 60
) · 100 = 2.5%
60 oz ± 2.5%
59. ( 5.25 ____ 175
) · 100 = 3%
175 km ± 3%
60. 6 in. + 5 in. = 11 in.
11 in. _____ 2 = 5.5 in.
6 in. - 5 in. = 1 in.
1 in. ____ 2 = 0.5 in.
Length tolerance: 5.5 in. ± 0.5 in.
3 1 __ 2 in. + 4 1 __
4 in. = 7 3 __
4 in.
4 1 __ 4 in. - 3 1 __
2 in. = 3 __
4 in.
3 __ 4 in. · 1 __
2 in. = 3 __
8 in.
7 3 __ 4 in. · 1 __
2 = 31 ___
4 in. · 1 __
2 = 31 ___
8 in. = 3 7 __
8 in.
Width tolerance: 3 7 __ 8 in. ± 3 __
8 in.
61. 730.56 mm - 6.5 mm = 724.06 mm730.56 mm + 6.5 mm = 737.06 mmThe circumference range is 724.06 mm-737.06 mm.538.5 g - 28.5 g = 510.0 g538.5 g + 28.5 g = 567.0 gThe mass range is 510.0 g-567.0 g.1358.5 mm - 63.5 mm = 1295.0 mm1358.5 mm + 63.5 mm = 1422.0 mmThe bounce height range is 1295.0 mm-1422.0 mmBasketball 4 meets all specified tolerances because its circumference is between the circumference range, its mass is between the mass range, and its bounce height is between the bounce height range.
62. Possible answer: Nearest 1 __ 2 -inch; the manufacturer’s
meas. is to the nearest in., so the actual meas. is
between 38 1 __ 2 in. and 39
1 __ 2 in. This means Linda’s
door must be at least 39 1 __ 2 in. wide.
63. No; the precision is too great because (1) the length of the cut boards cannot be known to a greater precision than the length of the orig. board; (2) if Yusuf measures the cut boards the same way he measured the orig. board, the precision will be the same; and (3) part of the length of the orig. board equal to the thickness of the blade used to cut it will be lost.
34 Holt McDougal Algebra 1
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StandardiZed teSt prep
64. 0.9728 g = 972.8 mgRounding 972.8 mg to the nearest milligram equals 973 mg. C is the correct answer.
65. 1.4 mm - 0.02 mm = 1.38 mm1.4 mm + 0.02 mm = 1.42 mm1.378 mm is less than the minimum tolerance of 1.38 mm. J is the correct answer.
66. 0.475 L = 475 mL0.5 L = 500 mLA tenth of a milliliter is smaller than a milliliter, so 475.3 milliliters is the most precise. A is the correct answer.
challenge and extend
67. 5.002 g - 5.000 g = 0.002 g
0.002 _____ 5.000
· 100 = 0.04%
68. 525.3(0.005) = 2.6525.3 mi - 2.6 mi = 522.7 mi525.3 mi + 2.6 mi = 527.9 mi522.7 mi-527.9 mi
69. 384,403(0.0002) = 77 km384,403 - 77 km = 384,326 km384,403 + 77 km = 384,480 km384,326 km-384,480 km
reAdY to go on? section b quiz
1. 2 __ 3 = x ___
18
36 = 3x
36 ___ 3 = 3x ___
3
12 = x12 laptop models were sold.
2. 150 pages
_________ 5 h
· 1 h ______ 60 min
= 1 __ 2 page/min
3. 156 Calories ___________ 26 crackers
= 6 Calories/cracker
4. 1024 photographs
_______________ 8 h
= 128 photographs/h
5. -18 ____ n = 9 __ 2
-36 = 9n
-36 ____ 9 = 9n ___
9
-4 = n
6. d __ 5 = 2 __
4
4d = 10
4d ___ 4 = 10 ___
4
d = 2.5
7. 4 ___ 12
= r + 2 _____ 16
64 = 12r + 24 ____ - 24 _______ - 24 40 = 12r
40 ___ 12
= 12r ___ 12
10 ___ 3 = r
8. -3 ___ 7 = 6 _____
x + 6
-3x - 18 = 42 ________ + 18 ____ + 18 -3x = 60
-3x ____ -3
= 60 ___ -3
x = -20
9. RT ___ XZ
= ST ___ YZ
8 __ n = 12 ___ 9
72 = 12n
72 ___ 12
= 12n ____ 12
6 cm = n
10. AD ___ FJ
= CD ___ HJ
1.45 ____ 2.9
= n ___ 0.5
0.725 = 2.9n
0.725 _____ 2.9
= 2.9n ____ 2.9
0.25 yd = n
11. 2.5 ft; a tenth of a foot is the smaller measurement
12. 3 ft; a foot is the smaller measurement
13. 5910 g; a gram is the smaller measurement
14. 16.0 oz; a tenth of an ounce is the smaller measurement
15. 300(0.01) = 3 300 - 3 = 297 300 + 3 = 303 297 m - 303 m
16. 150(0.06) = 9 150 - 9 = 141 150 + 9 = 159 141 lb - 159 lb
17. 60(0.005) = 0.3 60 - 0.3 = 59.7 60 + 0.3 = 60.3 59.7 L - 60.3 L
18. 220(0.015) = 3.3 220 - 3.3 = 216.7 220 + 3.3 = 223.3 216.7 kg - 223.3 kg
studY guide: reView
VaRiables and eXpRessiOns
1. literal equation 2. ratio 3. ratio
4. 1.99 g 5. t + 3
6. qp = (1)(5) = 5 7. p ÷ q = (5) ÷ (1) = 5
8. q + p = (1) + (5) = 6
9. 150 ÷ m
150 ÷ (5) = 30
150 ÷ (6) = 25
150 ÷ (10) = 15
sOlVing eqUatiOns by adding OR sUbtRaCting
10. b - 16 = 20 ______ + 16 ____ + 16 b = 36
11. 4 + x = 2 _______ - 4 ___ - 4 x = -2
12. 9 + a = -12 _______ - 9 ____ - 9 a = -21
13. -7 + y = 11 _______ + 7 ___ + 7 y = 18
14. z - 1 __ 4 = 7 __
8
_____
+ 1 __ 4
____ + 1 __
4
z = 9 __ 8
15. w + 2 __ 3
= 3
_____
- 2 __ 3
____
- 3 __ 2
w = 7 __ 3
16. Let s represent the number of signatures Robin still needs.
27 + s = 108 ________ - 27 ____ - 27 s = 81 Robin still needs 81 signatures for her petition.
35 Holt McDougal Algebra 1
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sOlVing eqUatiOns by mUltiplying OR diViding
17. 35 = 5x
35 ___ 5 = 5x ___
5
7 = x
18. -3n = 10
-3n ____ -3
= 10 ___ -3
n = - 10 ___ 3
19. -30 = n __ 3
(3)(-30) = (3) ( n __ 3 )
-90 = n
20. x ___ -5
= -2.6
(-5) ( x ___ -5
) = (-5)(-2.6)
x = 13
21. 5y = 0
5y
___ 5 = 0 __
5
y = 0
22. -4.6r = 9.2
-4.6r _____ -4.6
= 9.2 _____ -4.6
r = -2
sOlVing twO-step and mUlti-step eqUatiOns
23. 4t - 13 = 57 ______ + 13 ____ + 13 4t = 70
4t __ 4 = 70 ___
4
t = 17.5
24. 5 - 2y = 15 ________ - 5 ___ - 5 -2y = 10
-2y
____ -2
= 10 ___ -2
y = -5
25. k __ 5 - 6 = 2
_____ + 6 ___ + 6
k __ 5 = 8
(5) k __ 5 = (5)8
k = 40
26. 5 __ 6 f - 3 __
4 f + 3 __
4 = 1 __
2
12 ( 5 __ 6 f - 3 __
4 f + 3 __
4 ) = 12 ( 1 __
2 )
10f - 9f + 9 = 6 f + 9 = 6 _____ - 9 ___ - 9 f = -3
27. 7x - 19x = 6 -12x = 6
-12x _____ -12
= 6 ____ -12
x = - 1 __ 2
28. 4 + 3a - 6 = 43 3a - 2 = 43 ______ + 2 ___ + 2 3a = 45
3a ___ 3 = 45 ___
3
a = 15
29. 8n + 22 = 70 _______ - 22 ____ - 22 8n = 48
8n ___ 8 = 48 ___
8
n = 6
3n = 3(6) = 18
30. 0 = 6n - 36 + 36 _______ + 36 36 = 6n
36 ___ 6 = 6n ___
6
6 = n
n - 5 = 6 - 5 = 1
31. 180 = 3a + 2a - 25 180 = 5a - 25 ____ + 25 _______ + 25 205 = 5a
205 ____ 5 = 5a ___
5
41 = a The angles are 3a = 3(41) = 123° and 2a - 25 = 2(41) - 25 = 82 - 25 = 57°.
sOlVing eqUatiOns with VaRiables On bOth sides
32. 4x + 2 = 3x ________ - 3x ____ - 3x x + 2 = 0 _____ - 2 ___ - 2 x = -2
33. -3r - 8 = -5r - 12 ________ + 5r _________ + 5r 2r - 8 = -12 _____ + 8 ____ + 8 2r = -4
2r __ 2 = -4 ___
2
r = -2
34. -a - 3 + 7 = 3a -a + 4 = 3a _______ + a ___ + a 4 = 4a
4 __ 4 = 4a ___
4
1 = a
35. -(x - 4) = 2x + 6 -x + 4 = 2x + 6 _______ + x _______ + x 4 = 3x + 6 ___ - 6 ______ - 6 -2 = 3x
-2 ___ 3 = 3x ___
3
- 2 __ 3 = x
36. 2 __ 3 n = 4n - 10 ___
3 n - 1 __
2
2 __ 3 n = 2 __
3 n - 1 __
2
_____
- 2 __ 3 n
_________ - 2 __
3 n
0 = - 1 __ 2 7
no solution
37. 0.2(7 + 2t) = 0.4t + 1.4 1.4 + 0.4t = 0.4t + 1.4 ________ - 0.4t __________ - 0.4t 1.4 = 1.4 3 all real numbers
38. Let p represent the number of photos. 0.36p = 2.52 + 0.08p _______ - 0.08p ___________ - 0.08p 0.28p = 2.52
0.28p
_____ 0.28
= 2.52 ____ 0.28
p = 9 Juan has 9 photos to print.
36 Holt McDougal Algebra 1
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sOlVing fOR a VaRiable
39. C = 360 ____ n
(n)C = (n) 360 ____ n
nC = 360
nC ___ C
= 360 ____ C
n = 360 ____ C
40. S = n __ 2 (a + ℓ)
( 2 __ n ) S = ( 2 __ n ) n __ 2 (a + ℓ)
2S ___ n = a + ℓ
___ - ℓ _____ - ℓ
2S ___ n - ℓ = a
41. a = d __ g
(g)a = (g) d __ g
ag = d
ag
___ a = d __ a
g = d __ a
g = 75 ____ 20.2
g ≈ 3.7 gal
sOlVing absOlUte-ValUe eqUatiOns
42. ⎜x + 6⎟ = 21 Case 1 x + 6 = 21 _____ -6 ___ -6 x = 15 x = 15, -27
Case 2
x + 6 = -21
_____ - 6 ___ -6
x = -27
43. 7 ⎜y - 5⎟ = 14
7 ⎜y - 5⎟
______ 7 = 14 ___
7
⎜y - 5⎟ = 2
Case 1
y - 5 = 2
+ 5 _____ y =
+ 5 ___
7
y = 7, 3
Case 2
y - 5 = -2
_____ +5 ___ +5 y = 3
44. 3 ⎜y⎟ + 4 = 31
_________ - 4 ___ -4
3 ⎜y⎟ = 27
3 ⎜y⎟
____ 3 = 27 ___
3
⎜y⎟ = 9
y = -9, 9
45. 12 = ⎜x - 5.4⎟
Case 1
x - 5.4 = 12.0
______ + 5.4 _____ + 5.4
x = 17.4
x = 17.4, -6.6
Case 2
x - 5.4 = -12.0
_______ + 5.4 _____ + 5.4
x = - 6.6
46. ⎜g + 6⎟ + 12 = 14
__________ - 12 ____ -12
⎜g + 6⎟ = 2
Case 1
g + 6 = 2
_____ -6 ___ -6
g = -4
g = -4, -8
Case 2
g + 6 = -2
_____ -6 ___ -6
g = -8
47. ⎜x⎟ = 5 __ 7
x = - 5 __ 7 , 5 __
7
48. ⎜x - 55⎟ = 5 Case 1 x - 55 = 5 ______ + 55 ____ +55 x = 60x = 60,50
Case 2
x - 55 = -5
______ + 55 ____ +55
x = 50
minimum: 50 mi/h maximum: 60 mi/h
Rates, RatiOs, and pROpORtiOns
49. Let x represent the number of cups of rice you will need.
x ___ 10
= 2 __ 6
6 · x = 2 · 10 6x = 20
6x ___ 6 = 20 ___
6
x = 3 1 __ 3
You will need 3 1 __ 3 cups of rice to make 10 servings of
casserole.
50. 30 cm ______ s · 1 m _______ 100 cm
· 3600 s _______ 1 h
= 1080 m/h
51. 75 ft ____ s · 1 mi ______ 5280 ft
· 60 s _____ 1 min
≈ 0.85 mi/min
52. n __ 8 = 2 ___
10
10n = 16
10n ____ 10
= 16 ___ 10
n = 1.6
53. 2 __ 9
= 12 ___ x
2x = 108
2x ___ 2
= 108 ____ 2
x = 54
54. 3 __ k = 9 ___
15
45 = 9k
45 ___ 9 = 9k ___
9
5 = k
55. 1 __ 3
= x _____ x - 6
x - 6 = 3x ______ - x ___ - x -6 = 2x
-6 ___ 2
= 2x ___ 2
-3 = x
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appliCatiOns Of pROpORtiOns
56. AC ___ DF
= BC ___ EF
x ____ 11.5
= 2 ___ 9.2
9.2x = 23
9.2x ____ 9.2
= 23 ___ 9.2
x = 2.5 cm
57. Let x represent the height of the tree.
x ___ 14
= 2 ____ 1.75
1.75x = 28
1.75x _____ 1.75
= 28 ____ 1.75
x = 16 The tree is 16 ft tall.
58. Original radius: 9 in. A = π r 2 = π(9 ) 2 = 81π
New radius: 9 · 2 __ 3 = 6 in.
A = π r 2 = π(6 ) 2 = 36π
Radii: Original
_______ New
= 9 __ 6 = 3 __
2
Area: Original
_______ New
= 81π ____ 36π
= 9 __ 4 = ( 3 __
2 )
2
The ratio of the areas is the square of the ratio of the radii.
pReCisiOn and aCCURaCy
59. 12 in.; an inch is the smaller measurement
60. 37.0 g; a tenth of a gram is the smaller measurement
61. 550 cm; a centimeter is the smaller measurement
62. 1.5 L; a tenth of a liter is the smaller measurement
63. 500(0.04) = 20 500 - 20 = 480 500 + 20 = 520 480 lb - 520 lb
64. 20(0.005) = 0.1 20 - 0.1 = 19.9 20 + 0.1 = 20.1 19.9 oz - 20.1 oz
65. 75(0.03) = 2.25 75 - 2.25 = 72.75 75 + 2.25 = 77.25 72.75 kg - 77.25 kg
66. 1035(0.1) = 103.5 1035 - 103.5 = 931.5 1035 + 103.5 = 1138.5 931.5 mm - 1138.5 mm
chApter test
1. c - a = (6) - (2) = 4
2. ab = (2)(3) = 6
3. c ÷ a = (6) ÷ (2) = 3
4. c __ b =
(6) ___
(3) = 2
5. b - a = (3) - (2) = 1
6. five less than n; the difference of n and 5
7. 8n; 8(5) = 40 mi
8. y - 7 = 2 ____ + 7 ___ + 7 y = 9
9. x + 12 = 19 _____ - 12 ____ - 12 x = 7
10. -5 + z = 8 _______ + 5 ___ + 5 z = 13
11. 9x = 72
9x ___ 9 = 72 ___
9
x = 8
12. m ___ -8
= -2.5
(-8) ( m ___ -8
) = (-8)(-2.5)
m = 20
13. 7 __ 8 a = 42
( 8 __ 7 ) 7 __
8 a = ( 8 __
7 ) 42
a = 48
14. 15 = 3 - 4x ___ - 3 ________ - 3 12 = -4x
12 ___ -4
= -4x ____ -4
-3 = x
15. 2a ___ 3 + 1 __
5 = 7 __
6
30 ( 2 __ 3 a + 1 __
5 ) = 30 ( 7 __
6 )
20a + 6 = 35 _______ - 6 ___ - 6 20a = 29
20a ____ 20
= 29 ___ 20
a = 1.45
16. 8 - (b - 2) = 11 8 - b + 2 = 11 10 - b = 11 ________ - 10 ____ - 10 -b = 1 (-1)(-b) = (-1)(1) b = -1
17. -2x + 4 = 5 - 3x ________ + 3x ______ + 3x x + 4 = 5 _____ - 4 ___ - 4 x = 1
18. 3(q - 2) + 2 = 5q - 7 - 2q 3q - 6 + 2 = 5q - 7 - 2q 3q - 4 = 3q - 7 ________ - 3q ________ - 3q -4 = -7 7 no solution
19. 5z = -3(z + 7) 5z = -3z - 21 ____ + 3z ________ + 3z 8z = -21
8z ___ 8 = -21 ____
8
z = -2.625
20. r - 2s = 14 ________ - r ___ - r -2s = 14 - r
-2s ____ -2
= 14 - r ______ -2
s = r - 14 ______ 2
21. V = 1 __ 3 bh
V = h __ 3 b
( 3 __ h ) V = ( 3 __
h ) h __
3 b
3V ___ h = b
22. P = 2(ℓ + w)
P __ 2 =
2(ℓ + w) _______
2
P __ 2 = ℓ + w
____ - w _____ - w
P __ 2 - w = ℓ
23. ⎜x - 14⎟ = 21 Case 1 x - 14 = 21 _______ + 14 ____ +14 x = 35 x = 35, -7
Case 2 x - 14 = - 21 _______ + 14 ____ +14 x = - 7
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24. 3 ⎜x⎟ + 5 = 8 _______ - 5 ___ -5 3 ⎜x⎟ = 3
3 ⎜x⎟
____ 3 = 3 __
3
⎜x⎟ = 1 x = 1, -1
25. ⎜2v ⎟ = 6 Case 1 2v = 6
2v ___ 2 = 6 __
2
v = 3
Case 2 2v = -6
2v ___ 2 = -6 ___
2
v = -3
26. 120 ____ 25
= 4.8 sheets/student
27. 1300 mg
________ day
· 1g ________
1000 mg ·
365 days ________
1 yr
13
102
73
= 13 · 73 ______ 2 g/yr = 949 ____
2 g/yr = 474.5 g/yr
28. 5 __ 4 = x ___
12
60 = 4x
60 ___ 4 = 4x ___
4
15 = x
29. 8 ___ 2z
= 15 ___ 60
480 = 30z
480 ____ 30
= 30z ____ 30
16 = z
30. x + 10 ______ 10
= 18 ___
12
12(x + 10) = 18(10) 12x + 120 = 180 _________ - 120 _____ - 120 12x = 60
12x ____ 12
= 60 ___ 12
x = 5
31. Let d represent the distance between the two cities on the map in inches.
1 ____ 500
= d ____ 875
875 = 500d
875 ____ 500
= 500d _____ 500
1.75 = d The cities are 1.75 in. apart on the map.
32. EF ___ RT
= EG ___ RS
6 __ x = 5 ___ 20
5x = 120 x = 24 in.
33. HJ ____ WX
= LK ___ ZY
3.84 ____ 3.2
= 2.04 ____ x
3.84x = 6.528
3.84x _____ 3.84
= 6.528 _____ 3.84
x = 1.7 m
34. 6.5 oz; a tenth of an ounce is the smaller measurement
35. 16 oz; an ounce is the smaller measurement 36. 3525 m; a meter is the smaller measurement
37. 25(0.01) = 0.25 25 - 0.25 = 24.75 25 + 0.25 = 25.25 24.75 ft–25.25 ft
38. 400(0.04) = 16 400 - 16 = 384 400 + 16 = 416 384 lb–416 lb
39. 250(0.005) = 1.25 250 - 1.25 = 248.75 250 + 1.25 = 251.25 248.75 cm–251.25 cm
39 Holt McDougal Algebra 1
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