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(1)

2.1 Variables and Algebraic Expressions

1. x; 3 and 6

2. a and b; 3

3. t; 4 and 6

4. r; π_{and 2}

5. –8, –3, –1, 4

6. 2, 7, 9, 14

7. –12, 3, 9, 24

8. –4, 6, 10, 20

9. –2, 1

2, 3 2, 4

10. 4, 21

4 , 23

4 , 7

11. 0, 5, 21, 96

12. 1, 6, 9, 54

13. 8n

14. n – 17

15. n – 10

16. n + 24

17. 5n + 4

18. 2n + 6

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20. n

21. q5

22. s3

23. 325n

24. 2y (if y = Monique’s speed)

25. 3x + 4 (if x = the number of math books)

26. 2(24) + 2w or 2w + 48

27. 25x + 90y

28. p + q + r

30. a2 + b2

31. 2

7

n n+

32. 1 x

33. n + (n + 2) + (n + 4)

34. 126 – n(n + 1)

35. n(n + 2) – 3

36. 3(90 – a)

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Section 2.1 40. 4x + 4y + 2z

41. 3x + 2y + z

42. Sue: m + 6; Jim: m – 10

43. 4x – 2y + 4z

44. 0.06(24x + 4y) or 1.44x + 0.24y

45. Answers will vary. Possible answers: five more than two times a number; the sum of twice a number and five

46. Answers will vary. Possible answers: three times the

sum of a number and two; triple the result of

increasing a number by two

47. $0.01/day ≈_$0.43/mo ≈_$5.26/yr

48. $0.14/day = $4.32/mo = $52.56/yr

49. $0.10/day ≈_$2.85/mo ≈_$34.69/yr

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51. –24

52. –12

53. 108

54. 3

55. xaxb = xa + b

56. a

b

x

x = x

a – b

57. (xa)b = xab

58. x4

59. x10

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2.2 Evaluating Algebraic Expressions

1. –32

2. 12

5

3. –2

4. 12

5. –14

5

6. 12

7. 63 61

125 =

7936 125

8. –24

5

9. –59

10. 10

11. 13.856 psi

12. 46.4°_F

13. 160 ft

14. 50 in.

15. 12.56 ft

16. 40 in.3

17. 60 in.3

18. 336 in.3

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20. 8

49

21. a4

22. c5

23. 183

24. –1

25. –29

12

26. 3

16

7

28. –31

80

29. 94 mi

30. 121 lb; lose 33 lb

31. $22.50

32. $37.92

33. $715

34. $10,395

35. $155

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Section 2.2 39. d

r = t

40. p = c + 2l

41. d = 2r

42. Five is less than seven.

43. Pi is not equal to 3.14 (π ≈_3.14).

44. –1219

84

45. 25

4

46. 87.92 ft2

47. c is 1.5 times as large; A is 2.25 times as large.

48. $346.90/yr

49. $22.34/yr

50. The empty set is a subset of the natural numbers.

51. Negative one is not an element of the natural numbers.

52. Distributive Property

53. Associative Property of Multiplication

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55. Parentheses or grouping symbols, exponents,

multiplication and division left to right, addition and subtraction left to right

56. x9

57. y7

58. 4n

59.

2

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2.3 Using the Distributive Property

1. 3, 4, –5; 4y, –5y

2. 8, 3, 6, 8x2, 6x2

3. 1, –2, –9; xy, –2xy, –9xy

4. 1, –1, 3; x2yz, 3x2yz

5. 4x + 8y

6. –6z – 14

7. 5x2 + 5xy

8. 1

3xy – 3 2x

9. 10a

10. 6k

11. 16xy

12. 14ab

13. –3d + 10f

14. 2x2 + 8x

15. 3y2 – 8y

16. 3x2y + 14x2 – 4x

17. 6a + 9

18. –2x + 23

19. x – 8y

20. 2y

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22. 4b – 10c

23. 8x – 5y

24. –6a – 8b

25. 5a – 4b

26. 8m + 14n

27. b – 18

28. x – 47

29. –5.94m + 1.6n

30. 6.1x2 – 5.2x

31. 2x

32. – 6 5a

2₊12

5 a – 3z + 32

5 or

–1.2a2 + 2.4a – 3z + 6.4

33. x2 – y2

34. x2 + 2xy + y2

35. –9p – 17

36. –4r2 + 6r

37. –x3 – 13x2 + 12x

38. –6x3 – 30x2 – 11x + 27

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Section 2.3 40. 4y – 11

41. 4x2 + 2x – 15

42. a2 – 6

43. A = 1

2hb1 + 1

2hb2

44. p = 2l + 2w

45. Ft = m(v1 – v2)

46. C = 5

9F – 160

9

47. payback period = initial investment ÷_{savings per} period

48a. $4.20/yr; $26.28/yr

48b. ≈_{1.54 yr or 18.5 mo}

49a. $90

49b. ≈_{6.11 yr or 73.3 mo}

50. x + y

51. t – 5

52. x5

53. x + 6

54. 3x + y; 2.3

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56. Commutative Property of Addition

57. Multiplicative Identity Property

58. Associative Property of Addition

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2.4 Solving One-Step Equations

1. false

2. true

3. true

4. false

5. no

6. no

7. yes

8. yes

9. subtract 7; Addition Property of Equality

10. add 3; Addition Property of Equality

11. divide by 4; Multiplication Property of Equality

12. multiply by 5;

Multiplication Property of Equality

13. x = 9

14. x = –19

15. b = 76

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17. x = 5

2

18. y = –10

19. c = 72

20. x = 41

21. Multiplication Property of Equality

22. Multiplicative Inverse Property

23. Multiplicative Identity Property

25. x = 1

4

26. x = 118

35

27. y = 30

28. z = 11

29. b = 4.38

30. a = 0.49

31. d = 1.612

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Section 2.4 33. w = 1

18

34. x = 106

35. y = 20.5

36. z = 56.28

37. 4n = 20; n = 5

38.

15

n

= 120; n = 1800

39. 6r = 37.80; r = $6.30

40. t + 17 = 84; t = 67°

41. a + 115 = 180; a = 65°

42. a + 37 = 90; a = 53°

43. x = d + b

44. x = a b

45. x = nq

46. x = z – y

47. ROI = (savings ÷_initial investment) ×_100%

48. 64.9%

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50–51.

Z W

N

Q

Real numbers Q₉ 2.3

!64

52–53.

54.

5 4

x y

55. ₉1 ₂ a b

56. –18

57. –17

18

58. –x3 + 2y + 1; –14.4

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2.5 Solving Two-Step Equations

1. x = 8

2. y = –12

3. z = 5

4. b = 20

5. c = –8

6. d = 6

7. x = –355

8. y = 30

9. p = 96

10. n = 75

2

11. r = 3

12. s = 16

13. –41

14. 84

15. –83

16. 5

17. 14

18. 6 qt

19. 81 stamps

20. 6 in.

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22. a = –102

23. x = –1.9

24. b = 41

25. y = –4.81

26. c = 13.68

27. z = –39

20

28. d = –77

30

29. x = 23

32. 3

2

33. 13 nickels

34. 17 fives

35. 47 min

36. 14 T-shirts

37. 24 ft

38. 4 campers

39. 7.5 sec

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Section 2.5 42. 108 ft by 216 ft by 266 ft

43. take the square root of both sides

44. Yes; yes; both (₂7)2 and 72 equal 49.

45. No; no; neither (₂5)2 nor 52 equals ₂25.

46. taking a root

47. t = vf vi a

−

48. l =

2 S r r π π −

49. $612.96/yr

50. $367.90/yr

51. 0.61 yr ≈_{7.3 mo}

52. 163%

53. ₂19

54. ₂5

55. –144

56. –9

57. –13

58. –17

8

59. 6xy – 12y2

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61. –4x + 10

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2.6 Simplifying Equations

1. a = 1

2. b = –2

3. c = –6

4. d = 2

5. w = 9

6. x = 20

7. y = –14

8. z = 3

9. m = 4

10. n = –7

11. p = –55

12. r = –1

13. s = 2

14. t = 7

15. k = 5

16. j =

–6

17. 5

33

18. 9

11

19. 1784

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20. 1354

555

21. n + (n + 23) = 83; 30 and 53

22. n + (n – 12) = 40; 26 and 14

23. n + (n + 1) + (n + 2) = 84; 27, 28, and 29

24. n + (n + 2) + (n + 4) = 57; 17, 19, and 21

25. g + (g + 11) = 63; 26 girls and 37 boys

26. b + (3b – 2) = 26; 7 boys

28. 6 ft by 11 ft

29. camera: $49.50; calculator: $37.50

30. b + (2b + 4) = 22; Bill: 6 books; Jason: 16 books

31. 34, 5, and 1

32. s + (s + 7) = 31;

sister: 12; Kenny: 19

33. x + (x – 29) = 85

34. x – (85 – x) = 29

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Section 2.6 37. x =

2

m+ n

38. x = e ac bd b

− −

39. $1700

40. 3.4 yr

41. Answers will vary.

42. ∅

43. {10, 20}

44. {–13, –5, 1, 4, 9, 17}

45. {…,–5, 0, 5, 10, 15, 20, 30, 40, …}

46. {5, 10, 15, 20}

47. 135

48. 3

49. 9

2 = 4.5

50. 3

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2.7 Solving Multi-Step Equation

1. x = 2

2. x = 9

3. x = 3

4. x = 14.25

5. x = 1

6. x = 0

7. no solution

8. x = 4

12. n = 4

3

13. y = 13

14. x = 7

15. a = –9

16. _R; identity

17. m = –2

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Section 2.7 22. x = 0.07

23. _R; identity

24. b = 16

17

25. x = 1040

67

26. Distributive Property

27. Commutative Property of Addition

28. Distributive Property (in reverse)

29. Addition Property of Equality

32. 8n = n + 504; 72

33. 2n – 3 = 3n + 31; –34

34. n + 2(n + 2) = 4(n + 1) – 5; 5, 6, and 7

35. 4n = 3(n + 2) + 4; 10 and 12

36. 2x + 2(x + 14) = 2(x + 2) + 2(7x); 2 units by 16 units and 4 units by 14 units

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38. 3n = 8(n + 2) + 4; –4 and –2

39. r = ribbon length; r + 2 = 2r – 6; r = 8;

desired length: 10 in.

40. 1800 items

41. 26 items

42. 1500 items

43a. 4l + 400

43b. 27.5l

43c. 27.5l = 4l + 400; l ≈_{17 lawns}

44b. 25s = 19s + 60; s = 10 sweatshirts

44c. 29s = 19s + 60; s = 6 sweatshirts

44d. Answers will vary.

45. 1

46.

3 2

c d

47. –80

9 = –8 8 9

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Section 2.7 51. f + 24(3) = 89; 17 ft

52. 5a + a = 180; 150°_{and 30}°

53. 14

9

54. 23

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2.8 Eliminating Fractions and Decimals

1. x = 12

2. x = 1

3. x = 21

4. x = –4

5. y = 50

3

6. a = 3

7. b = –4

11. b = 5

12. x = 45

13. y = 1

14. a = 18

15. x = 14.77

16. Multiplication Property of Equality and Distributive Property

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Section 2.8 18. 5 (or d)

19. Associative Property of Multiplication

20. y = –49

2

21. a = 22

22. k = 1

4

23. m = 7

24. x = –3

25. x = –155

128

≈_–1.21

26. s = 18

27. a = 4.375

28. t = –6

29. x = 2

30. 14 nickels, 26 pennies, and 9 dollar bills

31. 3 tens, 4 fives, and 8 ones

32. 26 quarters and 208 pennies

33. 66 dimes, 13 nickels, and 52 pennies

34. 7 dimes and 27 nickels

35. 7 quarters and 11 dimes

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37. 6 rolls of nickels, 12 rolls of dimes, and 18 rolls of

quarters

38. x = 3c 2b ac

+

39. x = 4

2

bd − dpq

40. expense: 149b + 225,000; revenue: 179b

41. 179b = 149b + 225,000; b = 7500 bikes

42. expense: 161k + 250,000;

43. 199k = 161k + 250,000; k ≈_{6579 bikes}

44. Answers will vary.

45. 6a – 9b

46. x2 – y2

47. x = 26

21

48. x = –15 14

49. x = –2.8

(31)

Section 2.8 51. p = – 1

2

52. t = –2

53. b = – 1 5

(32)

Chapter 2 Review

1. x; 3 and –4

2. a, b, and c; 5

3. A constant is any fixed number, while a numerical coefficient is a constant factor in a term.

4. n(n + 2)(n + 4)

5. (90 – a) + (180 – a)

6. 20, 8, 13, 68

10. 1

11. 58

12. 144 ft

13. 24 ft

14. –4x2 + 3x

15. –9m + 3n

16. 6r2 – 2r – 6

(33)

Chapter 2 Review 21. yes

22. x = –21

80

23. y = 8.32

24. z = 450

25. a = 24

26. b = 13

8

27. k = 9

2

28.

x

=

20

3

29. d = –2

5

30. c = –20

31 v = –3

32. x = 6

5

33. x = –1

34. n = 2.4

(34)

37. Associative Property of Addition

41. 1

7r = 13; 91 papers

42. 0.95 = 19c; $0.05

43. 15d + 5 = 350; 23 CDs

44. 1.2t + 22 = 78.4; 47 therms

45. n + 4n = 155; 31 and 124

46. n + (n + 1) + (n + 2) = 234; 77, 78, and 79

47. 25m = 5m + 300; 15 lawns

48. (180 – a) = 3(90 – a); 45°

49. 8 nickels and 12 quarters

(35)

Sequences—Arithmetic Sequences

1. 2, 5, 8, 11, 14

2. 5, 7, 9, 11, 13

3. –12, –19, –26, –33, –40

4. 148

5. –260

6. not possible

7. An = An – 1 – 5

8. An = An – 1 + 11

9. An = 10n + 4