Solutions to the Odd Problems
The Basic Pg. 3 A. 1. 15
9. 30
11. 48
B. 1. 27
3. 25
13. 100000
19.
22 ,
13. 77
3  22 ,
3  24 ,
5. 29
15. 107
17. 547
5. 36
15. 1000000
23 ,
3. 18
7. 49
2  32 ,
24 ,
3  5  22 ,
C. 21. 120 23. 540
37. 1024
39. 243
25. 504
Fractions and Mixed Numbers
1. 4
1
2
3. 2
11. 1000
17. 121
7  23 ,
B.
9. 81
7. 28
1
4
5.
6  22 ,
7  32 ,
33 ,
23  32 ,
27. 1200
25 ,
3  52 ,
29. 1200
22  32 ,
3 5  23
34 ,
31. 16
5 32 ,
33. 64
35.256
Pg. 5 A. 2/3, 2/3,5/3,4/3,5/7,3/2,5/4,2/3
3
1
12
7. 7
2
17
Multiplication and Division of Fractions Pg. 7
A. 1. a.6
5. a.3
b.10
c.14
b.15
9. a.14
B. 11. 30
23.
c.15
d.54
b.44
c.63
d.30
13. 15
15. 24
17. 36
Adults
Teens
3. a.10
d.18
b.15
7. a.27
b.24
19. 24
21. 69
c.5
d.27
c.21
d .14
Children
Males
16
27
12
Female
32
9
12
Total
48
36
24
25. 32 ; 8/27
LCM and LCD Pg. 10 A. 1. a. 24 b. 18 c.12 d. 20
3. a.72 b. 90
5. a.120 b.360 c. 144 7. a.72 b.120 c.240
9. a.360 b.720
156
60
44
60
Addition and Subtraction of Fractions Pg. 13 A. 1. 2
3. 2
B. 11.
4
24
18
24
20
24
9
24
13.
54
60
35
60
5.
2
5
c.180
7.
5
9
1
9.
7
9
B. 17.
C. 25.
41.
5
6
11.
13
4
5
6
19.
52
5
13.
13
6
15.
21.
11
42
47
6
23.
53
44
17
41
29
17
37
27.
29.
31.
33.
12
36
48
36
120
43.
13
180
45.
35.
1
7
37.
8
144
39.
115
144
121
24
Some Facts About Divisibility Pg. 16 A. 1. 106 can’t be divided by 3 and 6
3. 402
can be divided by 3 and 6 5. 183420 can be divided by 3 and 6 7. 2040 can be divided
by 4 and 8
9. 1096 can be divided by 4 and 8
11. 1134, 183420,801171 can be
divided by 9 13. 1134,183420 can be divided by 18
Cross Multiplication Pg. 18 A. 1.
3
2
3.
9
4
5.
6
5
7.
21
3
9.
20
2
B. 11.
4
5
7
13
is more 13. is more 15.
is more 17.
is more
5
6
10
8
C. 19.
1
23
21.
6
20
23.
3
10
25.
4
45
Signed Numbers Pg. 20 A. 1. 5
B. 15. 8 17. -21 19. -6 21.-12
5. -16 7. -60 9. -6
11. 11
13. -5
Addition and Subtraction of Signed Numbers Pg. 22 A. 1. 10
7. -16
9. -32
B. 11. 4
13. -10 15. -6
17. 30 19. -2
C. 21. 1
23. -9
25. 28
27. 32
D. 29. 7
31. 1
33. -6
35. 150
3. -4
5. 0
Multiplication and Division of Signed Numbers Pg. 24 A. 1. 0
7. 0
B. 9. -6
11. -6
13. -8
15. -16
3. 0
5. 9
C. 17. -4
19. 3
21.
3
2
3. 76
23.
3
2
25. 
4
15
27. -15
Order of Operations Pg. 27 A. 1. -9 3. -6 5. -27
B. 7. 7 9. 79 11. 11
13. 1
15. -25 17. -5 19. -39
C. 23. 4 and -4 25. 16 and -16
27. 18
D. 29. -1 31. -14 33. -41
35. -10
E. 37. 81
39. -8
41. 33
43. 16
45. 98
47. 72
21. -23
2
49. -15
51. 33
53. 6
55. -1/2
Variables and Evaluation Pg. 29 1. -6
3. 10
5. -8
7. 6
9. 9
11. 25
-4 15. -81 17. -54 19. 2
21. 55
23. 4 25. 19 27. -29 29. 0
31. 3
33. -1
35. -2
37. -31 39. -8 41. 3/4 43. 1
45. 1
47. 4
49. -20
13.
Expressions Pg. 33 A. 1. 8x
3. -8x
5. 8x + 4
7. -3x + 3
9. 2x-5
11. 6B-2A
B. 13. 3x+15 15. 12x+20
17. 6x 19. 11x+42
21. -54x+76
23. 62x+68
25. 2B-2A
27. 9A-20B
C. 29. 41x - 12 31. 13x – 32
33. – 40x + 69
35. 29x – 12 37. 7x/12 39. –
29x/24 41. 240 bananas and 264 apples
Linear Equations I Pg. 36 A. 1. x=1 3. x=2 5. x=3/2
B. 7. x=3/2 9. x=3/5
11. x=-8
13. x=12 15. x=7
C. 17. x=-2 19.x=3
21. x=-1/3 23.. x=-2
D. 25. x=2/3 27. x=8/3 29. x=2
31. x=0
33. x=5
35. x=-1
Linear Equations II Pg. 39 A. 1. x=1 3.x=4 5.x=-3 7.x=4/3 9.x=-7/3
B. 11.x=15/4 13.x=1/2 15.x=-9/14 17.x=20/3 19.x=-4/3 21.x=15 23. x=490/9
25.x=12 27.x=11/70
C. 29. x=1 31.x=0
D. 33. Identity
35. Inconsistent
37. Identity
Linear Word Problems Pg. 43. A. 1. (x – 10)
3. 2(x +10)
5. 2[x + (x – 100)] = 4x – 200 7. 3x
9. 3x +8(x +4) 11. (50 – x) lbs of
cashews, cost (400 – 5x)
13. A gets $75, B gets $45
15. A gets $48, B
gets $14, C gets $58
17. A gets $19.20, B gets $57.60, C gets $43.20
19. $20
21. 12 gal.
23. $4,000 at 4% and $6,000 at 6%
25. $7,500 at each
27. 8 lbs. of peanuts, 4 lbs of cashews
29. 5 lbs. of peanuts and 10 lbs. of cashews
Literal Equations Pg. 45 A. 1. b=a-d+e
3. b= (e-d) / 2
7.y=5/(3x+6)
9. y=(5-3x)/6x
11.t=6w
13. t=6w+3
17. t=6(w-a)+3
19.t=[c(w-d)+b]/a
Inequalities
Pg. 48
1. x < 3
3. x < –8
5. x ≥ 3
–8
3
9. 3 ≤ x < 6
7. x ≥ –8
3
6
–8
13. No such x
15. –7 ≤ x ≤ –3
19. x < –3
–7
21. –4 ≤ x
–3
25. – 2/5 ≤ x
–2/5
5. b= (e-d)/(2+a)
15.t=(aw+b)/3
–3
3
11. –8 ≤ x < 1
–8
1
17. x < –2
–2
23. x ≤ –8/5
–8/5
–4
27. x ≤ – 7/2
–7/2
3
29. denominator: 3, x›-21,
31. Denominator: 6, x≤1,
35. denominator: 12, x≥11/34
39.-4<x<2
41. -4≤x≤1
33. Denominator: 8, x≤13/12.
37. Denominator: 12, x≥9/5
43. -4≤x<2
The Rectangular Coordinate System Pg. 51. 1. A(5, 0), B(–3 , 0), C(0, 4), D(0, –3),
E(4, 2), F(–5, 3), G(–4 , –5 )
3.
Y-axis
5. 3rd quadrant
7. Any ordered pairs with (+#, –#)
Linear Equations and Lines Pg. 54 1. y = 4 3. x = 3 5. y = 5/2 7. x = 5 9. y = 8/3
11. y = 3/2 13. x = 4
23.
25.
.
4
27.
29.
31.
33.
Systems of Linear Equations Pg. 57 A. 1. a.
3. c.
B. 5. (0, 3) 7. (2, 1)
C. 9. –x
11. x
13. –9y
D. 15. (2,1)
17. (3, 0)
19. (3, –3/2)
21. (1, 1)
25. (–2, –1)
27.(34, 72)
E. 29. Dependent
Systems of Linear Equations II Pg. 60 1. (1, 2)
7.
9.
3. (3, 0)
23. (–18, –25)
5. (3, –3/2)
11.
5
Linear Word Problems II Pg. 63 1. A gets $75, B gets $45 3. A gets $86, B gets $34
5. 4 lb –cashews, 8 lb–peanuts 7. $4,000 at 4% , $6,000 at 6% 9. $5/lb–cashews, $2/lb–
peanuts 11. $2/lb each 13. $5,000 at 4%, $8,000 at 5% 15. $3,000 at 4%, $9,000 at 5%
Exponents Pg. 65 A.1. 1/2 3. 1/8
19. x 8
B. 17. x 2
29. x11
31. x 6 y 3
C39. 32 x 2
21. x 2 y 7
23.
5. 1/27
9 4 13
x y
4
7. 1/64 9. 3/2 11. 1/18 13. 1/6 15. 7/12
25. x17
27. x 5 y 7
33. 4x 4 y 3 35. 2x 4 y 1
41. b x  5 43. e x  4
Scientific Notation Pg. 68 A. 1.2410
3.3.15 5.0.00000762
B. 9.5310 11.0.031 13.5890000000 15.0.0000000052
C. 17. 1.0  101
19. 2.0 102
21. 2.31105
23. 0.1 101 25. 2.0  102
7.0.00000593
27. 2.31106
29. 2.31x10-2
D. 31. 0.1 101  1.0 33. 1.0 101  0.1
35. 4 106 1.2 105  4.8 1011  0.000000000048
37.4x10-3x1.2x106=4.8x103=4800 39. 2.4  104  6  105  1.44  102  144
41.2.4x108x6x108=1.44x1017=144000000000000000
43.
2.4 104  6 105
 1.2 109  1200000000
1.5 104  8 104
45.
2.4 104  5 105
 1013  0.0000000000001
2
2
1.5 10  8 10
Polynomial Expressions Pg. 71 A 1. 2 and -2
3. 2 and 2
5. 40 and -40
7. 80 and 80
B 9. 1 and 7
11. 22 and 28
13. -16 and 16 15.-5x-8 17.-33x+28 19.-5x-61
2
2
21.  x  11x  7 23. 3x  26 x  20 25. 26 x 2  16 x  25
27. 12 x3  74 x 2  103x  10
29. 2xy, when x = –1 we get –2, when x= –1 and y = 2 we get -4. 31. 3x 2  6 xy -9
Polynomial Expressions Pg. 73 A. 1. 9x 4 3. 15x 5 5. 15x 3 7. 6x 9
B. 9. x6+x5+x4
C. 11. 12 x 2  74 x  63 13. 65 x 2  34 x 15.-14x2-5x+6
D. 19. x 2  2 x  35 21. x 2  12 x  35 23. 3x 2  7 x  40 25. 9 x 2  49
27.-32x3+8x2-56x+14 29.10x3+x2+22x+15 31. x 2  2 x  1 33. 25 x 2  40 x  16
35. 24 x3  20 x 2  24 x
37. 6 x3  7 x 2  9 x  2 39. x 3  1
41. x 5  1
Special Binomial Operations Pg. 75 A. 1. x 2  12 x  35 3. x 2  2 x  35 5. 6 x 2  2 x  20
7. 4 x 2  25 9. 12 x 2  19 x  21 11. 4 x 2  25 13. 45 x 2  2 x  8 15. 20 x 2  19 x  3
6
17. x 2  2 xy  35 y 2 19. 9 x 2  49 y 2
B. 21. 2 x 2  x  15 23. 16 x 2  2 x  3
C. 25. 5 x 2  12 x  35
27. 7 x 2  17 x  34
29. 7 x 2  36 x  5
31.-2x2-31x+38
33. 2 x 2  13x  1 35. 3x 2  26 x  40
Multiplication Formulas Pg. 77 A. 1. 399
3. 1599
5. 396
7. 2496
B.
9.
441
11.
1521
13.
9604
15.
10100.25
2
2
2
2
2
2
C. 19. x  49
21. 9 x  25
23. 49  9x
25. 4 x  9 y
27. 1  49 y 29. 100  81x 2
31. x 2  14 x  49
33. 9 x 2  30 xy  25 y 2
35. 4 x 2  4 xh  h 2
Polynomials Formulas II Pg. 83 See last section answers.
Factoring Out the GCF Pg. 80 A.1. 2
B. 9. 2(2  3 y )
11. 4(8 A  5B  3C )
13. 2 x(2  3x )
2 x 2 (2 x 2  4 x  1)
17.
D. 25. ( y  3)( y  2)
( x  2)( x  3)
.19.
23.
2( y  2)
C.21.
5. 2x
7. 4A2 B2
15.4A2B2(8B-5AB-3)
3. 4
5( x  3)
27. ( y  2)( y  3) 29. ( y  4)( y  1) 31. ( y  3)(2 y  1) 33. (2 x  3)(2 x  3)
35. (2  y )(5 y  3) 37. ( y  3x)(2 y  x) 39. ( x  4 y )(5 x  2 y )
Factoring Trinomials I Pg. 82 A. 1.  x  1 x  2
7.  x  4 x  2
9.  x  2 x  3
17.  x  2  x  12
B.
C.
19.  x  3 x  8
27.   x  2  x  7 
35.
D. 41. x 2  1 is prime
11.  x  6 x  1
21. Prime
29. 3  x  2 x  12
3x  x  2  x  8
3.  x  2  x  3
13.  x  4 x  5
31. 2 x2  x  3 x  3 33. 5x3  x  1 2 x  1
37.
39.
Prime
2
43. x  9 is prime 45. 4 x 2  25 is prime
9. ( x  1)(5 x  2)
17. ( x  2)(6 x  1)
23. (2 x  1)(3x  4)
3. ( x  1)(3x  1)
  x 12 y  x  3 y 
5. ( x  1)(2 x  1)
11. ( x  1)(3 x  2)
13 ( x  1)(3 x  2)
19. (2 x  1)(3x  2)
21. (2 x  3)(3x  2)
252.(2 x  3)(2 x  3)
B. 31. x( x  2)(2 x  1)
15. Prime
25.  x  6 x  6
23. Prime
Factoring Trinomials II Pg. 85 A. 1. ( x  1)(3 x  2)
7. ( x  2)(2 x  1)
15. (2 x  3)(3x  2)
5. x 2  x  2 is prime
27. (5 x  2)(5 x  2) 29. prime
33. 10 x(4 x  1)
Factoring Trinomials III Pg. 87 A. 1– 27, odd are factorable, 29 is prime
B. 31. x(2x+1)(x-2) 33. -10X(4X+1)
Substitution and Factoring Formulas Pg. 90 A. 1.  x  1 x  1
3(3  2 x )
7. 4( x  2)
13.
 4 x  5 16 x 2  20 x  25

9.  x  2  x 2  2 x  4

3.  2 xy 1 2 xy 1
5.
11.  2 x  3 y   4 x 2  6 xy  9 y 2 
15.
h 2  2h  10
7
B. 17.  x  1 x  1
19.  x  3 x  3
25.  2  9 xy  2  9 xy 
C.
31.
21.  5x  8 5x  8
27. 2  5x  3 y  5x  3 y 
 x  1  x 2  x  1
37.  x  5   x 2  5 x  25
33.
23.  2 xy 1 2 xy  1
29.Prime
3  y  9  3 y  y2 
35.
 4  y  16  4 y  y 2 
39.  x  10   x 2  10 x  100 
Applications of Factoring Pg . 92 A.1.6,-4,6
7
4
3.  , 7,
1
4
5.-108,-18,42
B. 7.+, – , – , +
9. – , + , – , +
11. +, + ,+ , –
C. 13. x =–1, 4
15. x = – 3, – 4
17. x = 3, – 3
19. x = 5, – 2 21 .x = – 1/2, 2
23. x = +1/2, –1/2
25. x = 2, 2
27.x = –1, – 5
29. x = 0, 4, –2
31. x = 0, 0, 4
33. x =0, 0, 2, -2
35. x = ½, –3
37. x = 0, 4
39. x = 2, – 2
Word Problems Pg . 96 A. 1. After 1 second and 3 seconds
3. a. After 1 second and
5 seconds
b. After 3 seconds
c. 144 ft
B. 5. x = 2 ft
7. x = 3 ft
9. x = 3 ft
11. x = 2 ft
13. x = 4ft
15.x = 3 ft
8