Chapter 2
AND INEQUALITIES
The Addition Property
2. Equations that can be written in the
()
32 210
6210
−−=
−− =
83 209
11 11
+= −
=
12 18
≠
False
d. 65 5 11
12 5 5 22
xx−=+
+=−+
10. Subtract 3 (or add 3).−
22. 10 4
10 10 4 10
14
x
x
−+=−−
=−
24. 41
44 14
3
n
n
n
−=−
−+=−+
=
26. 25 21
25 21 21 21
46
46
y
y
y
y
−=+
−− =+ −
−=
=−
28. 19 19
19 19 19 19
r
r
−=−
−+=−+
26
34. 13
88
11 31
z
+=−
11 3
−+=−
36. 1
96
4
z
+=
1
x
=−
44. 11
55
11
⎟
⎜⎟
⎜
⎝⎠
21 1
⎛⎞
⎟
⎜
−−− =−
⎟
⎜⎟
16.8 3.2 20
+=
27
50. 11
72
7727
21 30
n
=+
x
x
()
03232
−− =
64. 12 7
12 12 7 12
5
x
x
−+=−+
=
x
2.4 2.4 98.6 2.4
x
−+= +
x
28 Chapter 2 Linear Equations and Inequalities
The Multiplication
Property
8. Multiply by 3.
12. 88
88
y
−=
14.
21
10
w
(
)
20. 50 2
x
=−
=
(
)
12
43
−−
=
()
43 4 3
34 3
d
⋅=⋅−
29
28. 55
6
65 65
56 5
6
a
a
=
⋅=⋅
=
65 62
56 53
4
c
c
⋅=⋅
=
42. 872
x
−=
1.8 1.8
=
30
48. 520
8
85 820
x
=
()
214 4
=
62. 12
20
t
=
Check:
66. 166
2
x
⋅=⋅
()
0.2 40 8
=
31
2
23 23000
32 3
2000
r
r
r
=
⋅=⋅
=
Check:
54 8.5 457
⋅=
74. 1
2
1
32
x
=
Check:
1. The multiplication property of equality
0.x≠Since this assumption leads to a false
3. a. Answers may vary.
by Combining Properties
Exercises
2. 7813
788138
r
r
−=
−+= +
Check:
6. 25 3 34
25 25 3 34 25
39
39
c
c
c
c
−−= −
−=
−=
s
22 4
−− =−
32
10. 342
3
33 423
3
39
3
y
y
y
+=
+−= −
=
0
0
x
x
−=
−=
3
3
y
y
−=
−=
16. 4313
5
433133
5
416
5
d
d
d
−=
−+= +
=
8
314 14 10 14
8
324
8
83 8 24
y
y
y
+−=−−
=−
20. 43 21
721
721
aa
a
a
+=−
=−
−
=
22. 418
318
318
xx
x
x
=
=
510 25
5510 255
10 30
10 30
x
x
x
x
−=−
−− =− −
−=−
−−
=
33
22
3
z
=
−−
=
28. 36 6
44
3
nn
n
+=−−
=
=−
30. 753
73533
74 5
774 57
mm mm
m
m
−− =+ −
−=
−− =−
11
753
⎛⎞ ⎛⎞
⎟⎟
⎜⎜
−=+
⎟⎟
32.
()
324 2
342448
28
22 82
tt tt
t
t
−−= −−
−− =−
−− + =− +
32. Check:
(
)
(
)
36 2 46 2
−= −
34.
()
547 2
54714
5747714
aa
aa aa
−= +
−−= −+
Check:
(
)
(
)
59 4792
−−= −+
36.
()
523 4 3
56 8 3
13 6 3
55
2
xx
xx
xx
x
−−=−
− +=−
−=−
−−
=
Check:
(
)
(
)
5232 4 32
−−=−
38.
()()
5
961290
yy
+− −=
()
()
()()
5315 10 3 4 3 0
−+ −−+=
34
40.
()( )
95 3 132
9515 132
nn n
nn n
++=−+−
++=−−−
n
=
Check:
()
()
()()
52 10 4 25 15
⎢⎥
⎣⎦
⎡⎤
−−= −
()
7221122
722 11 22
92 11 22
9 2 11 11 11 22
913 22
aa
aa
aa
aa aa
a
−−+=+
+− = +
−= +
−− = − +
−=
()( )
74213 1112
⎡
⎤
−+−− = −+
⎣⎦
52. c
54. 16 3 31
315
t
t
−=
−=
56. 311
7
33 113
7
8
r
r
r
+=
+−= −
=
35
76318
7363318
46 18
466 186
yy
yy yy
y
y
−= −
−−= −−
−=−
−+=− +
10 10 5 55 10
h
−+ = −
62. 10 3 12 75
13 12 75
25 75
25 75
25 25
xx
x
x
+=
=
=
66.
(
)
15 10 8 105
15 80 10 105
5 80 105
xx
xx
x
+−=
+− =
+=
68. 1
30 40 4
30 40 10
30 40 40 40 10
10 10
tt
tt
tt tt
t
⎟
⎜⎟
⎜
⎝⎠
=−
−=−−
−=−
1.2 1.2
=
10 10 10
10 10 10 10 10
10 20
10 20
t
t
t
t
−+=−
−+−=−−
−=−
−−
=
()
()
3260612182430
2 1 2 6 10 14 18 22 26
x
x
−−
+
36 Chapter 2 Linear Equations and Inequalities
and Formulas
6. 13
10. 5
ax b
=
12.
2
ml
=−
3
332
223
3
wrst
wrst
⋅=⋅
=
16. 25
25
xx y x
−+ =−
18. 5210
ab
+=
22. 73
336 3
aabca
−−=−
26. PiV
PiV
VV
Pi
V
=
=
=
37
28. 22
2222
22
22
Pl ll w
Pl w
Pl w
−=−+
−=
−=
2
s
R
aa
a
s
⋅= ⋅
2
rrmv
34. 2
22
2
=
36.
()
APPrt
A
PPPPrt
=+
−=−+
4
44
Ps
Ps
=
=
40. a.
2
22
A
ab
A
=
+
⋅=⋅
b. 2 11.5 10
b
=⋅ −
42.
A
lw
=
10
xyz
−=
46. 3
ab
+=−
48. T
CP
P
CP T
TCP
=
=
=
38 Chapter 2 Linear Equations and Inequalities
=
516
116 116 116
116 516
x
z
zx
−
⋅= ⋅
+=
S
l
+
=
=
Involving Percent
2. In solving the percent problem “What is
8. 2.00 6 12x=⋅=
=
x
x
=
5.4
x
x
=
39
x
x
=
x
=
x
=
80.1
x
36. 0.19 $10,000 $1900x=⋅ =
x
x
=
0.333
x
x
=
=
x
=
x
=
40
(
)
(
)
$4000
x
=
x
x
=
=
(
)
40.5 2 6
x
x
+=⋅
=
()
$100 0.10 $100 $110.+=
$110 0.10 $110 $99−=
41
price. However, the 3% increase is applied
10. a.
21 10
61 10
x+<−
+<−
()
10. d. 97611
xx−≤ −
s
≤
30. 51
25 25 30 25
n
−+>−+
42
36. 43
a
<−
2
x
≤
721
t
−−
44. 2
3
46. 42
y
≤−
48.
2
144 14
2
y
+−≥−−
v
>
52. 36 4 0
36 36 4 0 36
y
y
y
−− >
−+− >+
54. 24 9 13 8
−<− +
56. 613 6
77
yy
y
−+>+
−>−
777 147
t
−+≤− +
60.
(
)
28 22
26
26
22
w
w
w
+<
<
<
43
62.
(
)
0.2 10 5 9
219
21191
28
d
d
d
d
−−>
−+>
−+−>−
−>
64.
()()
24 3 3 4
8318
83 3318
zz
zz
zz zz
−< +
<+
−<−+
66.
()
620
620
m
m
−−≤
−+≤
y
y
>
()()
34 2 23 6
12 6 6 12
12 12 6 6 12 12
6624
mm
mm
mm
mm
m
−≥ −
−≥−
−− ≥ −−
−≥−
≤
74. 211
4
333
zz z−<++
241
213
z
−<
86. 824
824
t
t
−−
44
88. 5644
566 446
542
54 442
mm
mm
mm mm
−+−≥−+−
−≥−−
−+ ≥−+ −
14
266126
x
+−≤ −
98. 52 20
552 205
215
215
t
t
t
−+ > −
>
102. 10 36 12 10,000
4320 10,000
x
x
+⋅⋅≥
+≥
2. a. Sometimes true. For instance, this statement
3.d=−