Chapter 2
Linear Equations and Inequalities in One Variable
2.1 Check Points
1. 512
55125
017
x
x
x
2. 2.8 5.09
2.8 2.8 5.09 2.8
02.29
z
z
z
The solution set is
2.29 .
3.
13
24
13 33
24 44
23
44
1
4
x
x
x
x
Check:
4.
8771064
310
33103
yy
y
y
The solution set is
13 .
5.
7126
xx
The solution set is
12 .
6.
3625
326225
65
66 56
11
xx
xx xx
x
x
x
Check:
3625
3(11) 6 2(11) 5
xx
Chapter 2 Linear Equations and Inequalities in One Variable
2.1 Concept and Vocabulary Check
1. solving
2. linear
2.1 Exercise Set
1. linear
2. linear
3. not linear
11.
419
44194
023
23
x
x
x
x
Check:
419
23 4 19
19 19
x
13.
812
88 128
020
20
z
z
z
z
28
z
Check:
28 13 15
15 15
The solution set is
28 .
13 11
24
x
x
Check:
13 24 11
13 13
The solution set is
24 .
17.
17 5
17 5 5 5
y
y
Section 2.1 The Addition Property of Equality
18.
21 4
21 4
y
y
19.
711
11 7
4
z
z
z
20.
18 14
14 18
4
z
z
z
21.
617
17 6
11
y
y
y
22.
829
29 8
y
y
23.
17
33
x
61 7
33 3
77
88
21
84
x
x
88 8
99
88
The solution set is 1
.
710 17
12 12 12
t
Chapter 2 Linear Equations and Inequalities in One Variable
26. 27
36
72
63
t
t
27. 39
42
3393
44 24
21
4
x
x
x
28. 37
510
73
10 5
7613
10 10 10
x
x
x
29. 13
54
31
45
y
y
The solution set is 11 .
20
30. 11
84
11
y
y
The solution set is
1.
8
31.
3.2 7.5
3.2 3.2 7.5 3.2
4.3
x
x
x
Section 2.1 The Addition Property of Equality
32.
2.7 5.3
5.3 2.7
w
w
33.
39
42
33 93
44 24
x
x
34.
37
510
76
10 10
13
r
r
35.
513
513
18
y
y
y
Check:
36.
11 8
11 8
x
x
37.
33
52
33
52
s
s
The solution set is
9.
10
38.
75
32
75
z
z
14 14
66
The solution set is
29 .
6
Chapter 2 Linear Equations and Inequalities in One Variable
39.
830 520
520 830
y
y
40.
90 35
35 90
55
t
t
t
41.
3.7 8
83.7
4.3
r
r
r
Check:
4.3 3.7 8
88
The solution set is
4.3 .
43.
3.7 3.7
3.7 3.7
m
m
44.
77
11 11
y
77
11 11
The solution set is
0.
Check:
611 3 511 14
66 3 55 14
14 14
The solution set is
11 .
46.
354 9
59
xx
x
47. 75 82 4 3 235
12 17
xxx
x
−+++−=+⋅
+=
Section 2.1 The Addition Property of Equality
48.
13 3 2 6 2 1 3 2 9
362 1321318
14 21
rrr
rrr
r
49. 7469
7649
yy
yy
50. 4353
433533
35
rr
rr rr
r
51. 12 6 18 7
12 18
6
xx
x
x
52. 20 7 26 8
20 7 8 26 8 8
20 26
ss
ss ss
s
53.
423 68
423188
xx
xx
46 54 8
46 46
The solution set is
12 .
70 3 60 1 9
036 1 9
369
Chapter 2 Linear Equations and Inequalities in One Variable
57.
23
32
xx
xx
x
59.
12 2
212
10
x
x
x
The number is 10.
60.
23 8
23 23 8 23
x
x
62. 25
377
22 52
377 77
7
37
xx
xx xx
x
64.
520, 650CS
520 650
CM S
M
According to the formula, 49% of U.S. college
freshman had an average grade of A in high
school in 2010.
This overestimates the value given in the bar
graph by 1%.
b.
0.8 25
0.8(40) 25
px
p
freshman had an average grade of A in high
school in 2000.
This underestimates the value given in the bar
graph by 2%.
b.
0.8 25
0.8(50) 25
px
p
Section 2.1 The Addition Property of Equality
67. a. According to the line graph, the U.S. diversity
index was about 55 in 2010.
b. 2010 is 30 years after 1980.
68. a. According to the line graph, the U.S. diversity
index was about 47 in 2000.
b. 2000 is 20 years after 1980.
69. – 71. Answers will vary.
72. The adjective linear means that the points lie on a
line.
76. makes sense
77. false; Changes to make the statement true will vary.
A sample change is: If ya b
, then yab.
80. false; Changes to make the statement true will vary.
A sample change is: If
318,x
then
18 6.
3
x
83.
6.9825 4.2296
6.9825 4.2296
2.7529
y
y
y
16 4
12
86.
37 25 1 37 10 2
xx xx
88.
7
89.
314 26
3(4) 14 2(4) 6
12 14 8 6
xx
Chapter 2 Linear Equations and Inequalities in One Variable
2.2 Check Points
1.
12
3
x
2. a.
484
484
44
121
21
x
x
x
x
The solution set is
21 .
c.
15.5 5
15.5 5
55
3.1 1
3.1
z
z
z
z
The solution set is
3.1 .
b.
7
28 4
447
28
x
x
b.
3
13
( 1)( 1 ) ( 1)( 3)
13
3
x
x
x
x
x
6
x
The solution set is
6.
6.
41525
4 1515 2515
440
440
y
y
y
y
Section 2.2 The Multiplication Property of Equality
7.
215 421
24154421
xx
xx xx
8. a. The bar graph indicates that the median weekly
earnings for men with a bachelor’s degree and
higher in 2013 was $1395. Since 2013 is 33
years after 1980, substitute 33 into the formula
for n.
b. 29 427
1442 29 427
1442 427 29 427 427
Mn
n
n
2.2 Concept and Vocabulary Check
1. bc
2. divide
5. multiplying; 5
3
1. 5
6
665
6
130
x
x
x
2. 4
7
774
7
28
x
x
3311
3
133
33
x
x
x
Check:
33 11
Chapter 2 Linear Equations and Inequalities in One Variable
4.
8
5
x
5.
535
535
55
7
y
y
y
Check:
57 35
35 35
The solution set is
7.
6.
642
y
7. 763
763
77
9
y
y
y
Check:
79 63
63 63
9. 28 8
28 8
z
z
28 28
The solution set is
7.
2
or
1
3.
2
10.
36 8
36 8
88
9
2
z
z
z
Check:
9
36 8 2
6
z
Check:
18 3 6
18 18
The solution set is
6.
12.
54 9
z
Section 2.2 The Multiplication Property of Equality
13.
86
86
88
x
x
14.
84
84
88
x
x
15.
17 0
17 0
17 17
0
y
y
y
Check:
17 0 0
00
The solution set is
0.
17.
212
3
32 3
y
18.
315
4
y
41
60 15
4
15 15
The solution set is
20 .
19.
7
28 2
7
22
28
772
x
x
Chapter 2 Linear Equations and Inequalities in One Variable
20.
5
20 8
885
20
558
x
x
21.
17
117
x
x
22.
23
123
x
x
23.
47
47 1( )
1( 47) 1( 1)( )
47
y
y
y
y
24.
51
51
11
51
y
y
y
Check:
45 9
5
5
5
x
Check:
10 50
10 50
10 10
5
x
x
x
Check:
Section 2.2 The Multiplication Property of Equality
28.
83 45
8345
545
xx
xx
x
29.
2111
211111
210
210
x
x
x
x
30.
2513
255135
28
x
x
x
31.
239
23393
212
x
x
x
32.
329
32292
311
311
x
x
x
x
The solution set is
11 .
3
Chapter 2 Linear Equations and Inequalities in One Variable
34.
3413
344134
39
39
y
y
y
y
35.
37 1
377 17
36
36
33
y
y
y
y
36.
257
25575
212
y
y
y
37.
12 4 3
12 3 4 3 3
94
94
z
z
z
z
The solution set is
9.
4
38.
14 5 21
14 21 5 21 21
z
z
14 14
The solution set is
7.
Section 2.2 The Multiplication Property of Equality
40.
55
55 55
10
10
x
x
x
x
41.
6212
6 12 2 12 12
6122
6126 26
yy
yy
yy
yyyy
42.
8310
833103
510
yy
yy y y
y
43.
3215
32 2152
515
515
zz
zz z z
z
z
The solution set is
3.
44.
2418
24 4184
zz
zz z z
45.
5212
52 2122
312
xx
xx x x
x
Chapter 2 Linear Equations and Inequalities in One Variable
46.
738
73 383
48
xx
xx x x
x
47.
8425
842 252
645
2
yy
yyyy
y
Check:
33
8425
22
12 4 3 5
88
The solution set is
3.
2
48.
5636
563 363
266
yy
yyyy
y
49.
65 5
65 5
555
zz
zzzz
z
77
The solution set is
2.
50.
63 2
55
1
zz
z
Check:
61 3 1 2
633
33
The solution set is
1.
51.
6142 2
6214 2
4214
xx
xx
x
Section 2.2 The Multiplication Property of Equality
52.
9264
926 646
32 4
xx
xxxx
x
53.
3152
3215
51
yy
yy
y
54.
3254
324 544
25
yy
yy yy
y
55. x
56.
x
x
Δ
x
Δ
59.
610
610
x
x
66
10
3
x
The number is
10
.
62. 8
7
x
x
Chapter 2 Linear Equations and Inequalities in One Variable
63. 4856
488568
x
x
64. 31023
310102310
x
x
65. 315 6
31515 615
x
x
66. 511 29
51111 2911
x
x
67.
5
25
n
M
n
68.
5
n
M
If you are 3 miles away from the lightning flash, it
will take 15 seconds for the sound of thunder to
reach you.
740 2.03 740 740
1502.2
A
A
740 3.3 740 740
A
years after 1980, substitute 33 into the formula
for n.
15 358
15(33) 358
Mn
M