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EXERCISES
For more practice, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Example 1
(page 100)
Example 2
(pages 100–101)
Example 3
(page 101)
Example 4
(page 102)
Graph each inequality.
1. y . 2x + 1
2. y , 3
3. x # 0
4. y # x - 5
5. 2x + 3y $ 12
6. 2y $ 4x - 6
7. y . 32 x + 13
8. 3x - 2y # 9
9. 5x . -y + 3
10. Cooking The time needed to roast a chicken depends on its weight. Allow at
least 20 min/lb for a chicken weighing up to 6 lb. Allow at least 15 min/lb for a
chicken weighing more than 6 lb.
a. Write two inequalities to represent the time needed to roast a chicken.
b. Graph the inequalities.
Graph each absolute value inequality.
11. y $ ∆2x - 1«
12. y # ∆3x« + 1
13. y # ∆4 - x«
14. y . ∆-x + 4« + 1
15. y - 7 . ∆x + 2«
16. y + 2 # P 12 x P
17. 3 - y $ -∆x - 4«
18. 1 - y , ∆2x - 1«
19. y + 3 # ∆3x« - 1
Write an inequality for each graph. In each case, the equation for the boundary
line is given.
20. y = -x - 2
1
21. 5x + 3y = 9
y
y
1
B
102-104
Apply Your Skills
22. 2y = ∆2x + 6«
x
2
y
2
⫺2
4 6
x
᎐4
᎐2
x
Graph each inequality on a coordinate plane.
23. 5x - 2y $ -10
24. 2x - 5y , -10
25. 34 x + 32 y . 52
26. 3(x - 2) + 2y # 6
27. 0.5x + 1.2y , 6
28. -3x + 4y . -6
29. 12 x + 23 y $ 1
30. ∆x - 1« . y + 7
31. y - ∆2x« # 21
32. 2(x + 3) + y $ 2
33. 14x 2 12y . 1
34. ∆x + 2∆ - 3 , y
35. 23x 1 2 # 29y
36. 0.25y - 1.5x $ -4
37. 8x - 4y $ -3
Chapter 2 Linear Relationships and Functions
Write an inequality for each graph.
38.
2
y
39.
y
40.
y
2
⫺4 ⫺2
2
x
2
y
41.
42.
1
᎐1
Reading Math
For help with reading
and solving Exercise 44,
see p. 105.
C
Challenge
x
2
⫺2
᎐2
x
y
43.
x
2
y
x
᎐2
x
44. Open-Ended Write an inequality that has (10, 15), (-10, 20), (-20, -25), and
(25, -10) as solutions.
45. Business To raise funds, the junior class plans to sell frozen yogurt cones and
sundaes. Each dessert contains one scoop of yogurt.
a. Write an expression to represent the number of scoops of yogurt used in
making c cones and s sundaes.
b. Suppose you have enough yogurt for 200 scoops. Write an inequality to
represent all the possible combinations of cones and sundaes.
c. Graph the inequality. Is the point (20, 50) a solution?
d. On your graph, find the point representing 60 cones and as many sundaes as
possible. What does the s-value of this point represent?
46. Writing When you graph an inequality, you can often use the point (0, 0) to
test which side of the boundary line to shade. Describe a situation in which you
could not use (0, 0) as a test point.
Graph each inequality on a graphing calculator. Then sketch the graph.
47. y # ∆x + 1« - ∆x - 1«
48. y . ∆x« + ∆x + 3«
49. y , ∆x - 3« - ∆x + 3«
50. y , 7 - ∆x - 4« + ∆x«
Lesson 2-7 Two-Variable Inequalities
102-104
Standardized Test Prep
Multiple Choice
51. The graph at the right shows
which inequality?
A. y . ∆x + 4« - 4
B. y . ∆x - 4« + 4
C. y , ∆x + 4« - 4
D. y , ∆x - 4« + 4
52. The graph of which inequality has its vertex at Q 2 1
2, 25 R ?
F. y , ∆2x - 5« + 5
G. y , ∆2x + 5« - 5
H. y . ∆2x + 5« - 5
I. y . ∆2x - 5« - 5
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53. Which inequality is NOT equivalent to the others?
A. y # 2
3x - 3
C. 2x - 3y $ 9
B. 3y # 2x - 9
D. 2x - 3y # 9
54. The graph at the right shows
which inequality?
F. y # -2.5x + 5
G. 2.5x + y $ 5
H. 2.5x + y , 5
I. 5x + 2y # 5
55. Which point(s) are solutions of the inequality 5x + 3y $ 2?
II. (-1, 0) and Q 0, 2 2
3R
I. (0, 0)
A. I only
Short Response
B. I and II
2
III. Q 0, 2
3 R and Q 1, 2 3 R
C. III only
D. II and III
56. At least 300 tornadoes occur in the United States each year. Write an
inequality to model the number of tornadoes that could occur during the
next x years. Describe the domain and range of the inequality.
Mixed Review
Lesson 2-6
Lesson 2-3
Graph each function by translating its parent function.
57. y = 2x + 5
58. y = ∆x« - 3
59. f(x) = ∆x + 6«
60. f(x) = x - 2
61. y = ∆x + 2«
62. y = ∆x - 1« + 5
Determine whether y varies directly with x. If so, find the constant of variation.
63. y = x + 1
64. y = 100x
65. 5x + y = 0
66. y - 2 = 2x
y
67. x 5 3
68. -4 = y - x
69. y = -10x
70. xy = 1
71. Commissions The amount of a commission is directly proportional to the
amount of a sale. A realtor received a commission of $13,500 on the sale of a
$225,000 house. How much would the commission be on a $130,000 house?
Lesson 2-2
Graph each pair of equations on the same coordinate plane.
72. y = x, y = -x + 5
102-104
Chapter 2 Linear Relationships and Functions
73. y = -2x + 1, y = 2x
74. y = 4x - 1, y = x