1. Solving Multi-Step Inequalities
ALGEBRA 1 LESSON 3-4
21. n 9
22. w < 3
23. t –1
24. d 6
25. n 2
26. k –4
27. s < 10
28. p > 3
29. x > 2
30. m > –
31. d < –1
32. y –1
pages 155–159  Exercises
1. d 4
2. m > –3
3. x > –2
4. n 3
5. q 4
6. h –2
7. a 3
8. b > 6
9. c < 2
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s + 8 and s ,
so the two equal sides
must be no longer
than 9.5 cm.
12. –6x + 9
13. j 1
14. b <
15. h > 5
16. x 3
17. y > –8
18. w 4
19. c < –7
20. r 2
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10. 8t and t ,
so the average rate of
speed must be at least
52.5 mi/h.
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2. Solving Multi-Step Inequalities
ALGEBRA 1 LESSON 3-4
33. k
34. v –4
35. q –2
36. r 1
37. x < 1
38. m > –8
39. v 2
40. Subtract 8 from each side.
41. Subtract 7 from each side.
42. Subtract y from each side
and add 5 to each side.
43. Add 2 to each side,
then multiply each side
by –5, and reverse the
inequality sign.
44. Subtract 3j from each side
and subtract 5 from each side.
45. Answers may vary. Sample:
Multiply q – 3 by 2, add 3q to
each side, add 6 to each side,
and divide each side by 5.
46. a. –3t –9, t 3
b t, t 3
c. The results are the same.
47. 6 – (r + 3) < 15, r > –12
(t – 6) 4, t 14 2 3
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3. Solving Multi-Step Inequalities
ALGEBRA 1 LESSON 3-4
49. 3(z + 2) > 12, z > 2
50. Answers may vary.
Sample: To solve
2.5(p – 4) > 3(p + 2),
first use the Distributive
Property to simplify each side.
The result is 2.5p – 10 > 3p + 6.
Then use the Subtraction
Property of Inequality.
Subtract 6 from each side
and 2.5p from each side.
The result is –16 > 0.5p.
Then use the Division
Divide each side by 0.5.
The result is –32 > p. So the
solution is –32 > p or p < –32.
51. a. i. always true
ii. always true
iii. never true
b. If the coefficients of the only
variable on each side of an
inequality are the same,
then the inequality will either
be always true or never true.
52. For x = the number of guests,
(0.75) x ;
x 80; at least 80 guests must attend.
53. a. maximum
b. no more than 135
54. B
55. E
56. F
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4. Solving Multi-Step Inequalities
ALGEBRA 1 LESSON 3-4
57. A
58. D
59. C
60. Answers may vary. Samples:
– x – 5 > 0, x < –15;
– x – , x –45
61. r < 5
62. m –2
63. s
64. n –2
65. s < 8
66. k
77. For x = number of hours
of work each month,
15x – ( ) ,
so to make a profit he must
work at least 80 h per month.
78. For x = amount of sales,
x , so to
reach her goal, she must
have at least $7000 in sales.
79. Add 2x to each side rather
than subtract 2x, so x
80. Distribute 4 to 2 as well as n,
so n > –7.
81. a. x >
b. x <
67. n > –2
68. r 1
69. x > 1
70. a
71. m 1
72. k 2
73. n –23
74. x 0
75. a < –6
76. c 4 3 4
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5. Solving Multi-Step Inequalities
ALGEBRA 1 LESSON 3-4
82. x is an integer between
–3 and 7, inclusive.
in.  14.2 in.
84. –2 h
86. a. 74 boxes
b. 5 trips
87. C
88. F
89. A
90. F
91. [2] Maxwell should continue
ordering from the current
92. m –4
93. y –8
94. x > –12
95. t –3
96. b < 27
97. w > –98
98. p > 1
99. d 7 h
101. –16
104. –16
supplier. Let x = number
of bottles Maxwell orders
per month. The cost from
the current supplier is 3x + 25.
The cost from the competitor
is 4x + 5. The inequality
4x x + 25 represents
the number of bottles of
shampoo for which the
competitor will be less
expensive. Since x = 20,
the competitor will not be
less expensive for orders
of 30 bottles or more.
(OR equivalent explanation)
[1] incorrect answer OR
insufficient explanation
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