Chapter 1,

Chapter 1,
continued
4. By comparing y1 and y2, you can find all values of x for
which y1ay2.
1. {x{ 5 Lesson 1.7
Investigating Algebra Activity 1.7 (p. 50)
2
25 24 23 22 21
2
0
2
3
4
1
0
1
1
2
3
4
3
0
1
2
25 24 23 22 21
2
3
4
5
e.
2
1
0
3
4
3
or
x 2 3 5 210
x 5 13
or
Check: {x 2 { 5 10
{13 2 3{ 0 10
{x 2 3{ 5 10
{27 2 3{ 0 10
1
1
2
3
4
5
1
2
2
25 24 23 22 21
3
4
5
2
0
or
x 1 2 5 27
x55
or
x 5 29
Check: {x 1 2{ 5 7
{5 1 2{ 0 7
{7{ 0 7
2
3
4
5
The solutions are xa22 or xq2.
1
0
1
2
3
757
or
3x 2 2 5 213
3x 5 15
or
3x 5 211
x55
or
x 5 2}
3
11
3
4
5
{31 2 3 2 2 2{ 0 13
11
{3(5) 2 2{ 0 13 }
{13{ 0 13 13 5 13 {3x 2 2{ 5 13
{15 2 2{ 0 13
1
The solutions are xa1 or xq3.
i.
{2{ 0 7
x 2 2 5 13
25 24 23 22 21
{x 1 2{ 5 7
{2 1 { 0 7
Check: {3x 2 2{ 5 13
1
h.
x1257
7 5 7
The solutions are 5 and 29.
The solutions are 24axa2.
g.
x 5 27
4. {3x 2 2{ 5 0
x 2 3 5 10
The solutions are 13 and 27.
3
25 24 23 22 21
5 5 5
5
The solutions are 1axa3.
f.
5 5 5
1
The solutions are 22axa2.
25 24 23 22 21
{25{ 0 5
3. {x 1 2{ 5 7
2
0
{x{ 5 5
{10{ 0 10
{210{ 0 10
10 5 10
10 5 10 The solutions are 24 and 2.
d.
or x 5 25
2. {x 2 3{ 5 10
3
25 24 23 22 21
x55
The solutions are 5 and 25.
5
The solutions are 1 and 3.
c.
Check: {x{ 5 5
{5{ 0 5
5
The solutions are 22 and 2.
25 24 23 22 21
1
b.
{211 2 2{ 0 13
{213{ 0 13
13 5 13
11
.
The solutions are 5 and 2}
3
3
5. {2x 1 5{ 5 x
25 24 23 22 21
0
1
2
3
4
5
2x 1 5 5 3x
The solutions are xa24 or xq2.
55x
or
2x 1 5 5 23x
or
5x 5 25
1. Sample answer: The solutions of the absolute value
x 5 21
equations in step 1 are two numerical solutions; no; the
equation {x{ 5 k has only 1 solution if k 5 0 and has no
solutions if k is negative.
Check: {2x 1 5{ 5 3x
{2(5) 1 5{ 0 3(5) {2(21) 1 5{ 0 3x
2. Sample answer: The solutions of absolute value
inequalities with aare ranges of values between and
including two numbers. The solutions of absolute value
inequalities with qare ranges of values outside and
including two numbers.
{x 1 { 5 x
{10 1 5{ 0 15 {22 1 5{ 0 23
{15{ 0 15
{3{ 0 23
15 5 15 3
T he solution is 5. Reject 21 because it is an
extraneous solution.
30
Algebra 2
Worked-Out Solution Key
Þ 23
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
a.
1.7 Guided Practice (pp. 53–55)
Chapter 1,
continued
12. {7 2 x{a4
6. {4x 2 1{ 5 2x 1 4x 2 1 5 2x 1 9 or
24a7 2 xa4
4x 2 1 5 2(2x 1 9)
2x 5 10
or
4x 2 1 5 22x 2 9
x55
or
6x 5 28
211a2xa23
11qxq3
3axa11
8
4
x 5 2}6 5 2}3
2
{41 2}3 2 2 1{ 0 21 2}3 2 1 9
4
{4(5) 2 1{ 0 2(5) 1 9
{19{ 0 19
{
{
that must be rejected because it does not satisfy the
original equation.
19
19
}5}
3
3
2. The absolute value of x is 2x if the actual value for x is
negative. For example, if x 5 24,
{x{ 5 4 5 224 5 2x
3. {213 2 1{ 0 14
x 1 4a26
x 1 4q6
xa210
210
26
22
xq2
2
Yes, 213 is a solution of the equation.
6
4. {24 1 6{ 0 10
x 2 7 < 21
2
x 2 > 2x < 6
2x > 8
x<3
x>4
3
4
5
6
9. {3x 1 5{q10
3x 1 5a210
3x 1 5q10
{2{ 0 10
2 Þ 10
No2is not a solution of the equation.
5. {32 2 6(22){ 0 20
{32 1 12{ 0 20
{44{ 0 20
44 Þ 20
No22is not a solution of the equation.
3xa215
3xq5
6. {2(28) 1 6{ 0 10
xa25
xq}5
{216 1 6{ 0 10
{210{ 0 10
3
2
13
25
{214{ 0 14
14 5 14 8. {2x 2 7{ > Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
1. An extraneous solution is an apparent solution
7. {x 1 4{q6
10.
12
Skill Practice
The solution is 5 and 2}43.
1 0
1.7 Exercises (pp. 55–58)
{2}{0}
19 5 19
4
8
2 0 2}3 1 9
2}
{20 2 1{ 0 10 1 9 8
{t 2 7.875{a0.375, the unacceptable mat
thickness is {t 2 7.875{ > 0.375.
{4x 2 { 5 2x 1 9
{x 2 { 5 2x 1 6
13. Because the acceptable mat thickness is
Check:
4
23
21
1
10 5 10 3
Yes, 28 is a solution of the equation.
7. {3(1) 2 7{ 0 4
{3 2 7{ 0 4
{24{ 0 4
{x 1 2{ < 6
26 < x 1 2 < 6
28 < x < 4
454
28
24
0
4
8
Yes, 1 is a solution of the equation.
8. {17 2 8(4){ 0 15
11. {2x 1 1{a
{17 2 32{ 0 15
{215{ 0 15
2ax 1 a
2axa
2ax a
15 5 15 25
26
22
2
6
Yes, 4 is a solution of the equation.
10
Algebra 2
Worked-Out Solution Key
31
Chapter 1,
continued
9. {x{ 5 9
19. {5 2 q{ 5 7
212
or
x 5 29
0
26
6
5 2 q 5 27
12
or
52q57
2q 5 212
or
2q 5 2
q 5 12
or
10. {y{ 5 25
The absolute value of a number cannot be negative.
No solution.
11. {z{ 5 0
24
z50
2
f52
0
2
4
or
f2553
or
f58
4
6
212
g2257
g 5 25 or
g59
0
26
6
h 2 5 2
h50
0
2
h2454
or
h58
6
8
k1356
k 5 29
or
k53
3
0
24
4
m 1 5 2
or
m1551
or
m 5 26
26
24
m 5 24
or
n 5 219
or
n 1 9 5 10
n51
1
219
0
26
6
18. {6 2 p{ 5 4
6 2 p 5 24
32
or
62p54
2p 5 210
or
2p 5 22
p 5 10
or
p52
0
4
4
or
2d 2 5 5 13
2d 5 28
or
2d 5 18
d 5 24
or
d59
or
3g 5 27
g 5 27 or
g 5 2}3
7
23. {7h 2 10{ 5 4
7h 2 10 5 24
or
7h 2 10 5 4
or
7h 5 14
or
h52
24. {3p 2 6{ 5 21
3p 2 6 5 221
or
3p 2 6 5 21
3p 5 215
or
3p 5 27
p 5 25
or
p59
or
2q 1 3 5 11
2q 1 3 5 211
2q 5 214
or
2q 5 8
q 5 27
or
q54
4r 1 7 5 243
n 1 9 5 210
212
0
26. {4r 1 7{ 5 43
0
22
17. {n 1 9{ 5 10
218
24
r 5 28
25. {2q 1 3{ 5 11
16. {m 1 { 5 28
28
6
or
29
or
h 5 }7
k 1 3 5 26
28
r50
7h 5 6
15. {k 1 3{ 5 6
212
2r 5 8
3g 5 21
12
or
4
24 2 r 5 4
or
3g 1 14 5 27 or 3g 1 14 5 7
14. {h 2 4{ 5 or
22. {3g 1 14{ 5 7
25
212
12
2r 5 0
2d 2 5 5 213
or
8
21. {2d 2 5{ 5 13
8
13. {g 2 2{ 5 7
g 2 2 5 27
4
20. {24 2 r{ 5 4
12. {f 2 5{ 5 3
f 2 5 5 23
0
24 2 r 5 24
0
22
24
q 5 22
8
Algebra 2
Worked-Out Solution Key
12
16
4r 5 250
r 5 212.5
or
4r 1 7 5 43
or
4r 5 36
or
r59
27. {5 1 2j{ 5 9
5 1 2j 5 29
or
5 1 2j 5 9
2j 5 214
or
2j 5 4
j 5 27
or
j52
28. {6 2 3k{ 5 21
6 2 3k 5 221
or
6 2 3k 5 21
23k 5 227
or
23k 5 15
k59
or
k 5 25
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
x59
Chapter 1,
continued
29. {20 2 9m{ 5 7
36. {8x 2 1{ 5 6x
20 2 9m 5 27
or
29m 5 227
m53
30.
29m 5 213
13
m5}
9
1
x 5 228
14x 5 1
or
2x 5 1
or
x 5 }2
or
1
}x 2 3 5 10
4
{
1
or
} x 5 13
or
x 5 52
{8x 2 1{ 5 6x
{1 2 { 1
6
8
{}14 2 1{ 0 }14
1
4
2
{81 }2 2 2 1{ 0 61 }2 2
1
6
1
{4 2 1{ 0 3
0 14
14 {
{2}
{
{3{ 0 3
}
3
7
3
7
3 5 3
}5}
or
1
}y 1 4 5 6
2
} y 5 210
or
}y52
y 5 220
or
y54
1
2
1
1
and }2.
The solutions are }
14
1
2
37. {4x 1 5{ 5 2x 1 4
2
}z 2 6 5 12
3
{
8x 2 1 5 6x
1
1
8}
21 06 }
14
14
1
}y 1 4 5 6
2
1
} y 1 4 5 26
2
{
4x 1 5 5 22x 2 4
or
4x 1 5 5 2x 1 4
6x 5 29
or
2x 5 21
or
x 5 2}2
9
x 5 2}6
2
}z 2 6 5 12
3
2
}z 2 6 5 212
3
2
}z 5 26
3
2
}z 5 18
3
z 5 29
z 5 27
3
Check: {4x 1 5{ 5 2x 1 4
{41 2}2 2 1 5{ 0 2 1 2}2 2 1 4
3
values will produce a negative numerical value.
or
3x 2 4 5 x
4x 5 4
or
2x 5 4
x51
or
x52
Check: {3x 2 4{ 5 x
{3(1) 2 4{ 0 1
{3 2 4{ 0 1
{21{ 0 1
151
{3x 2 4{ 5 x
3(2)
2 4{ 0 2
{
{6 2 4{ 0 2
{2{ 0 2
151
3
{26 1 5{ 0 23 1 3
{21{ 0 1
34. {3x 2 4{ 5 x
3x 2 4 5 2x
1
x 5 2}2
33. No, {5x 2 10{ 5 245 has no solutions. No absolute
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
or
Check: {8x 2 1{ 5 6x
1
4
8x 2 1 5 26x
1
x5}
14
{}4x 2 3 {5 10
} x 5 27
32.
or
or
1
}x 2 3 5 210
4
31.
20 2 9m 5 7
252
{4x 1 5{ 5 2x 1 4
{41 2}2 2 1 5{ 0 21 2}2 2 1 4
1
1
{22 1 5{ 0 21 1 4
{3{ 0 3
353
3
1
The solutions are 2}2 and 2}2.
The solutions are 1 and 2.
35. {x 1 24{ 5 27x
x 1 24 5 7x
or
24 5 6x
or
45x
or
Check: {x 1 24{ 5 27x
{4 1 24{ 0 27(4)
{28{ 0 228
28 Þ 228
x 1 24 5 27x
24 5 28x
23 5 x
{23 1 24{ 5 27(23)
{21{ 0 21
{21{ 0 21
21 5 21 The solution is 23. Reject 4 because it is an
extraneous solution.
Algebra 2
Worked-Out Solution Key
33
continued
38. {9 2 2x{ 5 10 1 3x
41. When the equation was written as two equations, the
9 2 2x 5 210 2 3x
or
x 5 219
or
negative sign was not distributed properly.
9 2 2x 5 10 1 3x
{5x 2 9{ 5 x 1 3
21 5 5x
1
2}5 5 x
Check: {9 2 2x{ 5 10 1 3x
{9 2 2(219){ 0 10 1 3(219)
{9 1 38{ 0 10 2 57
{47{ 0 247
47 Þ 247
{9 2 2x{ 5 10 1 3x
{
{
6x 5 6
or
x51
47
15
1
{
1
or
x 5 2}6
28
15
0 7 2 1 2}
2
{
4
75 0
15
71}
82}
4
4
{
{
43
43
4
43
} 5 }
43
6
6
7
3x 1 7 5 5x
7 5 2x
10
or
na
or
10
11
12
7
35
{2}8 1 7{ 5 2}8 21
35
35 5 2}
8
8
35
35
} Þ 2}
8
8
{ {
}
7
The solution is }2.
Algebra 2
Worked-Out Solution Key
or
da27
or
28
{3x 1 7{ 5 5x
31 }
1 7 5 51 2}8 2
8 2
{
d 1 4a23
}5x
Check: {3x 1 7{ 5 x
{
6
n 2 11a21
7
2
or
27
2
22
n 2 11 q
nq12
13
47. {d 1 4{q3
or
or
2}8 5 x
9
9
40. D; {3x 1 7{ 5 5x
3x 1 7 5 25x
7 5 28x
8
46. {n 2 11{q1
43
} 5 }
15
1
and 2}6 .
The solutions are 2}
4
4
25
26
43
43
4
{
0
24
25 < m < 9
6
{}6 {0 }6
10
27 < m 2 2 < 7
0 7 2 1 2}1 2
5
1
8 2 }6 0 7 1 }6
{
{2}4 { 0 }4 43
1 2{
1
6
8 1 5 2}
6
45. {m 2 2{ < 7
{8 1 5x{ 5 7 2 x
2{
2
22
44. {k{ > k < 2or k > 4
8 1 5x 5 7 2 x
6x 5 21
{8 1 5x{ 5 7 2 x
15
4
5
25
Check:
8 1 5 2}
2aja
26
or
or
555
43. {j{a
39. {8 1 5x{ 5 7 2 x
x 5 2}
4
{2 2 7{ 0 6 2 1
{25{ 0 5
10 Þ 210
extraneous solution.
8 1 5x 5 27 1 x
4x 5 215
n 2 7 5 3n 2 1
2 2 7 0 3(2) 2 1
{210{ 0 29 2 1
{210{ 0 210
47
47
5
5
1
}
The solution is 2 5. Reject 219 because it is an
34
or
x53
Check: {n 2 7{ 5 3n 2 1
{23 2 7{ 0 3(23) 2 1
}5}
4x 5 12
extraneous solution.
{
{
47
6x 2 9 5 23
The solutions are 1 and 3.
{}5 { 0 }5
5x 2 9 5 2x 2 3
or
3
2
9 1 }5 0 10 2 }5
or
4x 2 9 5 3
42. The solution 23 does not work; it is an
1
1
9 2 21 2}5 2 0 10 1 31 2}5 2
5x 2 9 5 x 1 3
{
{
7
7
31 }2 2 1 7 5 51 }2 2
{ {
35
35 5 }
2
2
35
35
} 5 }
2
2
0
22
22 < f 1 6 < 2
28 < f < 24
35
}
24
dq21
48. {f 1 6{ < 2
{}2 1 7{ 5 }2
21
26
d 1 4q3
210
28
26
24
22
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Chapter 1,
Chapter 1,
continued
57. {7 2 2r{ < 49. {g 2 1{ > 0
g21>0
or
2(g 2 1) > g > or
2g 1 1 > 0
2 < 2 r < 2 < 2r < 12
13 > r > 26 l 26 < r < 13
g<1
13
22
0
21
1
2
50. {h 1 10{a
51.
218
212
26
t>}
5
{w 2 15{ < 30
2.4
230 < 3w 2 15 < 30
0
215 < 3w < 45
59.
25 < w < 15
0
25
5
xa28
or
xq2
12axa28
0
60.
4
8
6
1
1
26 < }3m 2 15 < 6
1
9 < }3m < 21
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
2a4ya16
27 < m < 63
2
27
3
20
4
61.
54. {5z 1 1{ > 14
5z 1 1 < 214
or
5z 1 1 > 14
5z < 215
or
5z > 13
or
13
z>}
5
z < 23
63
0
3
40
0
2
1
7
} y 1 2 < 28
16 2 p > 3
or
2p > 213
or
p < 13
17
19
280
62.
} y < 210
or
}y > 6
y < 270
or
y > 42
42
0
240
40
80
2
2
5
}n 2 8a2
211a24 2 qa11
2
5
235a2qa213
35qqq13 laqa
13
1
7
{}5n 2 8{ 1 4q12
2
{}5n 2 8{q8
56. {24 2 q{a11
or
2
5
}n 2 8q8
2
5
}na0
or
}nq16
na0
or
nq40
35
220
8
}y 1 2 > 8
1
7
4
1
7
or
270
or
60
1
55. {16 2 p{ > 3
15
50
{}7 y 1 2{ 2 5 > 3
1
{}7 y 1 2{ > 8
2.6
13
32
1
1
}aya4
2
11
24
{}3m 2 15{ < 6
27 a 4y 2 9 a 7
p > 19
8
1
53. {4y 2 9{a7
19 < p
6
{}2x 2 10{a4
2x 1 6q10
0
24
16 2 p < 23
12
2
2xq4
22
t<}
5
6a}1xa14
or
24
or
2
or
1
4
15
2xa216
0
25t > 212
24a}1 x 2 10a4
10
2x 1 6a210
28
19 2 5t > 7
or
5.2
2
52. {2x 1 6{q10
212
1 8
or
25t < 226
0
26
12
19 2 5t < 27
220
224
6
58. {19 2 5t{ > 7
2ah 1 a
2aha
0
26
16
4
2
32
0
20
40
60
40
Algebra 2
Worked-Out Solution Key
35
Chapter 1,
continued
63. C; {6x 2 9{q33
6x 2 9a233 or
x 2 9q33
xq42
6xa224 or
xa24
or
21 < x < 5
74.
65. Two solutions: c > 0
One solution: c 5 0
No solution: c < 0
66. {x 1 1{q216
The absolute value cannot be a negative number, so this
inequality is true for all real numbers.
0
22
2
4
The absolute value cannot be a negative number, so this
inequality is never true. There is no solution.
68. The absolute value cannot be a negative number, so the
only solution(s) will satisfy the equation {7x 1 3{ 5 0.
or
x<}
a
7x 1 3 5 0
{
2 110.25 { a
0.4
Ideal
Actual
a Tolerance
2
pH
pH
{
{
76. a.
h
{
p
6.5 {a
2
{
Actual
weight
2
Ideal
weight
{
w
2
0.85
3
5
{a
0.05
b. 20.05aw 2 0.85a0.05
0.8awa0.9
x 5 18
2
27
0
27
The pill can make up between about 15.2% and 18%
of the baseball’s total weight, inclusive.
x29>0
or
2(x 2 9) > 0
x>9
or
2x 1 9 > 0
77. Acceptable weights:
{w 2 21{a1
Weights that should be rejected:
x<9
6
9
{w 2 21{ > 1
12
78. a. Nearsightedness
Mild: 21.5x < x 1 1.5 < 1.5
2c < ax 1 b < c
23 < x < 0
2c 2 b < ax < c 2 b
Moderate: 21.5 < x 1 4.5 < 1.5
2c 2 b
c2b
}<x<}
a
a
71. ax 1 ba2c
or
26 < x < 23
ax 1 bqc
Severe: 21.5 < x 1 7.5 < 1.5
axa2c 2 b
or
axqc 2 b
2c 2 b
xa}
a
or
c2b
xq}
2caax 1 bac
2c 2 baaxac 2 b
2c 2 b
c2b
a
a
c2b
2c 2 b
}axa}
a
a
}qxq}
36
a Tolerance
90 5 5x
69. {x 2 9{ > 0
72.
{
x
0.9
5}
Maximum: }
100
5
The solution is x 5 2}7 .
70.
x ø 15.2
3
3
1
80 5 5.25x
x 5 2}7
0
{
a Tolerance
{
7x 5 23
21
c2b
x
0.8
c. Minimum: } 5 }
100
5.25
{7x 1 3{a0
ax > c 2 b
Ideal
Actual
2
height
height
75.
67. {2x 2 1{ < 225
or
2c 2 b
x>}
a
Problem Solving
23 < x 2 2 < 3
24
ax 1 b > c
ax < 2c 2 b
xq7
64. C; {x 2 2{ < 3
or
Algebra 2
Worked-Out Solution Key
a
29 < x < 26
Farsightedness
Mild: 21 < x 2 1 < 1
0<x<2
Moderate: 21 < x 2 3 < 1
2<x<4
Severe:21 < x 2 5 < 1
4<x<6
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
73. ax 1 b < 2c
Chapter 1,
b.
continued
Quiz 1.6 –1.7 (p. 58)
Nearsightedness
severe
210
mild
26
22
moderate
moderate
2
1. 4k 2 17 < 27
4k < 44
6
mild severe
k < 11
Farsightedness
8
30 1 60
90
79. Mean of extremes 5 } 5 } 5 45
2
2
{
{
t
{
3
550 1 650
2
15
1200
2
5
{
t
{
a Tolerance
212
24
25
23
r < 27
211
29
27
5. 3(x 2 7) < 6(10 2 x)
3x 2 21 < 60 2 6x
Tolerance 5 12,000 2 6008 5 5992
9x 2 21 < 60
{f 2 6008{a5992
9x < 81
1000 1 91,000
Mouse: means of extremes 5 }}
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
28
28r > 56
50
12,016
5}
5 6008
2
210
4. 28r 2 11 > 45
16 1 12,000
2
x<9
92,000
5}
5 46,000
2
Tolerance 5 91,000 2 46,000 5 45,000
{f 2 46,000{ a45,000
4
6.
6
8
10
1 2
225 2 4z > 66 2 17z
225 1 13z > 66
13z > 91
82. a. 20.05xax 2 250a0.05x
and
26
29pa81
81. Elephant: Mean of extremes 5 }
b. 20.05xax 2 250
11
pq29
{a
600
2
9
7
3. 29p 1 15a96
Tolerance 5 650 2 600 5 50
{
12
nq7
a Tolerance
80. Mean of extremes 5 } 5 }5 600
Mean of
Actual
2
extremes
temperature
11
14nq98
{a
45
2
10
2. 14n 2 8q90
Tolerance 5 60 2 45 5 15
Mean of
Actual
2
extremes
temperature
9
z>7
x 2 250a0.05x
250a1.05x
and
0.95xa250
238ax
and
xa263
The actual water depth could range from about 238 feet
to about 263 feet.
Mixed Review for TAKS
83. B;
28(5) 1 6x 5 2(130)
6x 5 120
x 5 20
Anne and her friend washed 20 cars.
84. H;
2(908) 1 2(1158) 1 mŽBCD 5 5408
mŽBCD 5 1308
4
6
8
10
1 2
7. {x 2 6{ 5 9
x 2 6 5 29
or
x 5 23
or
x2659
x 5 15
8. {3y 1 3{ 5 12
3y 1 3 5 212
or
3y 5 215
or
3y 1 3 5 12
3y 5 9
y 5 25
or
y53
or
2z 1 5 5 9z
or
5 5 7z
or
}5z
9. {2z 1 5{ 5 29z
2z 1 5 5 29z
11z 1 5 5 0
11z 5 25
5
7
5
z 5 2}
11
Algebra 2
Worked-Out Solution Key
37
Chapter 1,
continued
4. G; 34 1 3x 5 112
Check:
5
1 5{ 0 291 2}
{21 2}
11 2
11 2
5
{
45
{
0}
11 45
11
45
} 5 }
{
45
0 2}
45
7
2}
7
10
35
}1}
7
7
{
4he solution is2}
Reject }
because it is an
11
7
11
5
}Þ
5
extraneous solution.
or
p < 29
or
p17>2
p > 25
{2q 2 3{a3
15.95
5. C; } ø 5.4
2.95
If you rent at least six videos, you will save money.
6. H; d 5 depth (ft)
0 5 12 2 1.5t
1.5t 5 12
t58
The pool will be empty in 8 hours.
0a2qa6
7. C; Choice A: sides 2, 4, 9 l 2 1 4 > 9 0aqa3
Choice B: sides 3, 6, 9 l 3 1 6 > 9 12. {5 2 r{q4
Choice C: sides 5, 10, 9 l 5 1 10 > 9 5 2 ra24 or
5 2 rq4
2ra29 or
rq9
5 1 9 > 10 2rq21
or
ra1
Final
Final a0.8 + Current 1 0.2 + exam
grade
grade
score
85 a0.8 + 83
1 0.2 +
x
85a66.4 1 0.2x
18.6a0.2x
10 1 9 > 5 8. Let x 5 hours doing office work.
Let y 5 hours doing outside work.
Equation 1: 8x 1 9y 5 399
Equation 2: x 1 y 5 45 l x 5 45 2 y
Substitute for x in Equation 1:
8(45 2 y) 1 9y 5 399
y 5 39
93ax
You need to get a final exam score of 93 or better.
14. Acceptable weights for the container:
{w 2 1.5{a0.025
20.025 a w 2 1.5 a 0.025
1.475 a w a 1.525
Mixed Review for TEKS (p. 59)
1. B; Let c 5 gallons in city.
Let h 5 gallons on highway.
Equation 1: 60c 1 51h 5 675
Equation 2: c 1 h 5 12 l c 5 12 2 h
Substitute for c in Equation 1:
60(12 2 h) 1 51h 5 675
29h 5 245
h55
Five gallons of gas were used on the highway.
You worked 39 hours outside that week.
1
9. a 1 b 1 } (a 1 b) 5 72
2
3
2
3
2
} a 1 } b 5 72
3
2
} (a 1 b) 5 72
a 1 b 5 48
1
1
medium 5 }2 (a 1 b) 5 }2 (48) 5 24
The second longest piece is 24 inches long.
Chapter 1 Review (pp. 61– 64)
1. In a power, the exponent represents the number of times
the base is used as a factor.
2. If substituting a number for a variable in an equation
results in a true statement, then the number is a solution
of the equation.
3. An extraneous solution is an apparent solution that
2. J;
{w 2 3.5{ a 0.25
3.5 2 0.25awa3.5 1 0.25
3.25awa3.75
3. A; 2369aTa2297
38
45
The kicker made 26 field goals.
d 5 12 2 1.5t
p 1 7 < 22
23a2q 2 3a3
13.
7
x 5 26
t 5 time (h)
10. {p 1 7{ > 2
11.
3x 5 78
5
Algebra 2
Worked-Out Solution Key
must be rejected because it does not satisfy the
original equation.
4. Like terms: 3x 2 and 2x 2; 40 and 27
1
5. Sample answer: 5x 1 10 and 101 }
2x 1 1
2
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
10
55
2}
1}
11
11
5
{21 }7 2 1 5{ 0 291 }7 2