Download Chapter 2 Linear Equations and Inequalities in One Variable Exercise Set 2.1

Chapter 2
54. Mistake: Did not distribute the with the 4.
Correct: 2
Linear Equations and Inequalities
in One Variable
56. c 2 a 2
58.
I
Pr
A
2π r
Exercise Set 2.1
2.
A solution set is a set containing all of the
solutions for a given equation.
60.
4.
{ } or ∅
64. 6.
Subtract b from both sides.
8.
6
68.
10. 2
12. 8
16. 2
72.
18. 2
20. 1
22. 9
24. 1
26. 5.8
28. 1
30. 2
32. 2
34. 1
74.
t
αt
2
h
62.
ω
66.
P 2π r
2
70. y
14. 3
b2
3V
π r2
B
1 rt
h
P
d
9 4x
3
h h0
16
t2
2 E mgy m
v2
76. Mistake: Subtracted b instead of dividing by b.
A
Correct: h
b
78. Mistake: Did not multiply both sides of the
2A
b
equation by 2. Correct:
h
Exercise Set 2.2
2.
Answers will vary. Some possible answers:
Draw a picture. Make a table. Underline key
words. Search for a related example.
38. 10
4.
n + 2, n + 4
40. 84
6.
0.30 40 n or 12 0.30n ml
42. 1.8
8.
128.2° F
44. 2.6
10. 6850 sq. ft.
46. No solution
12. $1500
48. All real numbers
14. 3
50. Mistake: The distributive property was not used
correctly.
13
Correct:
3
16. 1
7
36. 2
52. Mistake: Subtracted before distributing into the
5
parentheses. Correct: 2
18. 3
20. $19,720
22. $40.83
24. $27,840
6
Chapter 2 Linear Equations and Inequalities in One Variable
26. 83, 84
10. a)
28. 53, 55, 57
^ x x ! 3`
b)
3, g c)
30. 23.75º, 66.25º
32. 65º, 115º
34. Categories
1 gallon
1/2 gallon
Value
Number
Amount
x
14.50 x
13
7
13x
7 14.50 x 36. Categories Rate
38.
Janet
45
Paul
50
Time
d
45
d 10
50
2½
®
12. a) ¯a a u ¾
3¿
°
« 2 ·
b) ¬ , g ¸
­ 3 ¹
c)
Distance
d
14. a)
d 10
Concen- Vol. of
Vol. of
Solutions trate
Solution
Acid
45%
0.45
x
0.45 x
35%
0.35
80 x 0.35 80 x 40%
0.40
80
0.40 80
^ s s e 3.2`
b)
g, 3.2@
b)
> 7, g ^ x ! 6`
b)
6, g ^ y y ! 2`
b)
2, g c)
16.
a)
^ x x u 7`
c)
40. $9 for the 1 gal. and $5.50 for the ½ gal.
42. 8:00 PM.
18. a)
44. 40 L of each
c)
46. Desktops are $1360 and laptops are $1620.
48. 17 Trivial Pursuit games and 34 Monopoly
games
50. 2.5 hours
20. a)
52. 5:00 PM
c)
54. 15 oz.
56. 100 ml
13 ½
®
22. a) ¯c c ! ¾
3¿
°
Exercise Set 2.3
2.
For x < a, the value of a is not included in the
solution set. For x e a , the value of a is included
in the solution set.
4.
All real numbers less than or equal to 4 are part
of the solution set.
6.
The direction of an inequality symbol changes
when both sides of the inequality are multiplied
or divided by a negative number.
8.
a)
c)
^ n n e 7`
b)
g, 7 @
¨ 13 ·
b) © , g ¸
ª 3
¹
c)
24. a)
c)
^ q q 19`
b)
g,19
Instructor’s Solutions Manual
26.
a)
^ b b u 16`
7
b) >16, g 42. a)
b)
g, g c)
c)
28. a)
^ a | a is a real number`
^ k k ! 3`
b)
^
b) > 0, g 3, g 44. a)
^`
or ˆ
b) No interval notation
c)
c)
30. a)
`
a au0
46.
2
x ! 8; x ! 12
3
48. 3 x 2 10; x 4
50. 3 2 x u 17; x e 7
c)
52. 3 x 4 8 u 16; x u 4
32. a)
^ v v u 8`
b)
> 8, g 54. lower than 73
56. 161 or higher
58. 3.5 ft. or more
c)
60. ≈ 3.8 cm or less.
62. 6.4 hours or more
17 ½
®
34. a) ¯ x x ! ¾
4¿
°
¨ 17 ·
b) © , g ¸
ª4
¹
64. 125 or more
66. a) t 1535 C
b) t u 1535°C
68. 2500 kg or less.
c)
Puzzle Problem
5½
®
36. a) ¯ p p ¾
3¿
°
5·
¨
b) © g, ¸
ª
3¹
^ b b e 3`
b)
g, 3@
c)
40.
a)
c)
Collaborative Exercises
2.
c)
38. a)
There is no conflict in what they said; therefore,
because “at least” one lied, they both must have
lied; therefore, the brother is older.
^f
`
f e 2
b)
g, 2@
Yes, because 40% off the price of lenses means a
customer pays 60% of the regular price, which
would be 0.6L.
4.
F 0.6 90 e 125; F e $71
6.
60 0.60 L 0.75 60 L ; L ! $100
8.
80 0.60 L 0.85 80 L ; L ! 48
Exercise Set 2.4
2.
and and or
4.
For two sets A and B, the union of A and B,
symbolized by A Š B , is a set containing each
element in either A or B.
8
6.
8.
Chapter 2 Linear Equations and Inequalities in One Variable
We graph the region included in either of the two
inequalities.
a. ^ 2, 4, 6`
b. ^ 2, 4, 6,8,10`
12. a. ∅
b. ^ a, e, h, l , m, o, t , v`
40.
a)
10. a. ^14,16`
b. ^ 8,10,12,14,16,18`
14. a. ^ c, d , e`
b) ∅ or
18. 0 e m 3
20. 1 r e 1
22. 7 t 15
c) no interval notation
42.
a)
b. ^ a, b, c, d , e, f `
16. 3 e n 7
^`
b)
^ x 0 e x e 4`
c)
> 0, 4@
^ x 4 x 6`
c)
4, 6
44.
24.
a)
b)
26.
46.
a)
28.
® 2
½
b) ¯ x e x e 3¾
° 5
¿
«2 º
c) ¬ ,3»
­5 ¼
48.
30.
a)
32.
b)
a)
^ x 2 x 4`
c)
2, 4
^ x 6 e x e 0`
c)
> 6, 0@
50.
b)
^ x 4 x 7`
c)
a)
4, 7
34.
b)
a)
b)
52.
^ x 4 e x 8`
c)
> 4,8
54.
36.
a)
b) ∅ or
^`
56.
c) no interval notation
38.
a)
b)
58.
^ x 2 e x 3`
c)
> 2,3
Instructor’s Solutions Manual
9
60. a)
76.
a)
b)
^ a a e 2 or a u 6`
c)
g, 2@ Š > 6, g b)
^ x 1 x e 4`
c)
1, 4@
^ x 5 e x e 3`
c)
> 5, 3@
^ x 1 x 2`
c)
1, 2
^ x 2 x e 1`
c)
2, 1@
^ x 4 e x e 3`
c)
> 4,3@
78.
a)
62.
a)
b)
b)
c) (g, 1) Š (3, g)
^ t t e 3 or t u 2`
80.
c) (g, 3] Š [2, g )
a)
64.
a)
b)
b)
^ x x e 4 or x u 1`
82.
a)
c) (g, 4] Š [1, g )
b)
66.
a)
b)
84.
^ q q e 2 or q u 3`
a)
c) (g, 2] Š [3, g)
b)
68.
a)
b)
^ x x 1 or x ! 3`
86.
a)
^ x x e 5 or x u 4`
c) (g, 5] Š [4, g)
b)
70.
88.
a)
b)
a)
^ y y u 1`
c)
> 1, g b)
72.
c) > 6,8@
a)
b)
^ d d 3`
c)
g,3
90.
a)
74.
a)
b)
c)
^ x 6 e x e 8`
b)
^ k k is a real number` , or
g, g ^ x 48 e x 88`
c)
> 48,88
10
Chapter 2 Linear Equations and Inequalities in One Variable
92. a)
b)
28. 0, 4
^ x 68° e x e 72°`
c) > 68, 72@
32. 1, 3
94. a)
b)
c)
1
30. , 1
5
34. 0, 10
^
x 40 mph e x e 70 mph
5 15
36. ,
2 2
`
> 40, 70@
38. 1, 5
40. 3, 5
96.
a)
42. 9, b)
^ x 0°C x 100°C`
c)
0,100
Puzzle Problem
20 km/hr. e r e 22.9 km/hr.
Exercise Set 2.5
7
3
3
2
44. 0,
46. all real numbers
48. 3
50. 22, 12
52. 15, 3
2
,2
5
2.
We are to find numbers that are 5 units from 0.
4.
There is no solution.
6.
After the absolute value equation is separated
into two equations, one with the two expressions
equal and the other with the two expressions
opposite, one of the equations leads to a
contradiction.
56. 5,5
2.
x e a or x u a
10. no solution
4.
Shade to the left of – a and to the right of a.
12. 3, 5
6.
when a < 0
14. 2, 6
8.
a)
8.
16. 1,
54.
Exercise Set 2.6
7
3
1 3
18. ,
2 2
26 22
,
3 3
b)
^ y 3 e y e 3`
c)
^ m 3 m 7`
c) 3, 7 > 3,3@
10.
a)
20. no solution
22.
5
3
24. 1, 1
26. 9, 3
b)
Instructor’s Solutions Manual
11
28.
12.
a)
a)
b)
^ p 1 e p e 7`
c)
> 1, 7@
b)
^ x x e 3 or x u 8`
c) (g, 3] Š [8, g)
14.
30.
a)
b)
a)
^ x 5 x 1`
c)
5, 1
5
®
½
b) ¯h h or h ! 2¾
3
°
¿
16. a)
5·
¨
c) © −∞, − ¸ ∪ 2, g ª
3¹
13 ½
®
¨ 13 ·
b) ¯h 3 h ¾ c) © 3, ¸
ª
5¿
5¹
°
32.
a)
18.
b)
a)
b)
^`
^ m m 2 or m ! 2`
c) (g, 2) Š (2, g)
or ˆ
c) no interval notation
34.
a)
20.
a)
b)
^ n 5 e n e 1`
c)
22. a)
b)
> 5,1@
^ x x e 0 or x u 4`
c) (g, 0] Š [4, g)
36.
a)
b)
c)
^ h h e 6 or h u 6`
g, 6@ ∪ > 6, g b)
^ x x e 8 or x u 4`
c)
g, 8@ Š > 4, g 24.
38.
a)
a)
b)
^ a a 1 or a ! 7`
c) (g,1) Š (7, g)
26.
b)
^ y 0 e y e 3`
c) > 0,3@
^ b b is a real number`
c)
40.
a)
a)
b)
^ x x e 14 or x u 4`
c) (g, 14] Š [4, g)
b)
g, g 12
Chapter 2 Linear Equations and Inequalities in One Variable
42.
a)
b)
^ u 6 e u e 2`
c)
> 6, 2@
^ p 4 p 0`
c)
4, 0
44.
a)
b)
46.
a)
b) ∅
c) no interval notation
48.
a)
b)
^ x 8 e x e 20`
c)
> 8, 20@
50.
a)
b)
^ y y 4 or y ! 8`
c) (g, 4) Š (8, g)
52.
a)
b)
^ w w e 0 or w u 15.9`
c)
g, 0@ ∪ >15.9, g 54.
a)
b)
^ p p is a real number`
56. x e 5
58. x u 2
60. x 3 ! 2
62. x 1 e 4
64. x any negative number
c)
g, g