(Solution Manual) Intermediate Algebra An Applied Approach

Aufmann, Lockwood, 9

Math & Statistics

Solution Manual

9th Edition

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Solution Manual for Intermediate Algebra An Applied Approach, The downloadable file consists of 619 pages, and the total size of the file is 8.6 MB. Purchase now only for highly discounted price.

Author(s): Aufmann, Lockwood

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Chapter 1: Review of Real Numbers Prep Test 1. 3013 303133 6039 6014 6025 307 125/g32/g152/g152/g32/g32/g14/g32/g14 2. 6011 6021 6032 207 158/g32/g16/g32/g16 3. 92 3523225 154 65/g32/g152/g152/g152/g152/g152/g32/g152 4.32 235522 25 154 52 154/g32/g152/g152/g152/g152/g32/g152/g32/g121 5.8.000 + 29.340 + 7.065 = 44.405 6.92.00 – 18.37 = 73.63 7.2.19(3.4) = 7.446 8.32.436 0.6 324.36 6 54.06/g121/g32 /g121 /g32 9.a) −6 > − 8 Yes b) − 10 > −8 No c) 0 > − 8 Yes d) 8 > − 8 Yes 10. C 5.021/g32 BAD 89.01008975.0437.0107 /g32/g32/g32 Section 1.1 Concept Check 1.a) integers: 0, −3 b) rational numbers: 33.2,3,0,215/g16/g16c) irrational numbers: 7,45..., 232232223.4,/g83 d) real numbers: all 2.a) integers: − 17 b) rational numbers: 21.6,9127, 03412.17/g16 c) irrational numbers: ... 010010001.1,3/g16/g83 d) real numbers: all 3. 32 4. –π 5. 45.1/g16 6.0 7.5.6 8.–6 9.Ͳ 10.–41 11.–54 12.–42 Objective A Exercises 13.Replace ywith each element in the set to determine if the inequality is true or false. −6 > − 4 False −4 > − 4 False 7 > − 4 True NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .2 Chapter 1 Review of Real Numbers 14.Replace xwith each element in the set to determine if the inequality is true or false. −6< −3 True −3 < − 3 False 3 < − 3 False 15.Replace wwith each element in the set to determine if the inequality is true or false. −2 <−1 True −1 <−1 True 0 <−1 False 1 <−1 False 16.Replace pwith each element in the set to determine if the inequality is true or false. −10 > 0 False −5 >0 False 0 > 0 True 5 > 0 True 17.Replace bwith each element in the set then evaluate the expression. − (−9) = 9 −(0) = 0 −(9) = − 9 18.Replace awith each element in the set then evaluate the expression. − (−3) = 3 − (−2) = 2 −(0) = 0 19.Replace cwith each element in the set then evaluate the expression. |−4| = 4 |0| = 0 |4| = 4 20.Replace qwith each element in the set then evaluate the expression. |−3| = 3 |0| = 0 |7| = 7 21.–x> 0 whenever the value of x is a negative real number. 22.Since | y| will always give us a nonnegative result there is no real number y for which −|y| > 0. Objective B Exercises 23.{−2, − 1, 0, 1, 2, 3, 4} 24.{−3, −2, − 1} 25.{2, 4, 6, 8, 10, 12} 26.{1,3, 5, 7, 9, 11, 13} 27.{3, 6, 9, 12, 15, 18, 21, 24, 27, 30} 28.{−20, −16, −12, −8, − 4} 29.{x|x> 4, x integers} 30.{x|x<–2,x integers} 31.{x|x>−2} 32.{x|x<2} 33.{x| 0 < x< 1} 34.{x| - 2 < x< 5} 35.{x| 1<x<4} 36.{x| 0< x<2} 37.Yes 38.No 39.No 40.Yes 41.No 42.Yes 43. {x| x< 2} ) -5 -4 -3 -2 -1 0 1 2 3 4 5 44. {x| x< −1} ) -5 -4 -3 -2 -1 0 1 2 3 4 5 NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.1 3 45. {x| x>1} [ -5 -4 -3 -2 -1 0 1 2 3 4 5 46. {x| x<−2} ] -5 -4 -3 -2 -1 0 1 2 3 4 5 47. {x| −1 < x< 5} ( ) -5 -4 -3 -2 -1 0 1 2 3 4 5 48. {x| 1 < x< 3} ( ) -5 -4 -3 -2 -1 0 1 2 3 4 5 49. {x| 0 < x<3} [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 50. {x| −1 <x<1} [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 51.(−2, 4) 52.(0, 3) 53.[−1, 5] 54.[0, 3] 55.(−∞, 1) 56.(−∞, 6] 57.[−2, ∞) 58.[3, ∞) 59.{x| 0 < x< 8} 60.{x| −2 < x< 4} 61.{x| −5 <x<7} 62.{x|3 < x<4} 63.{x|–3 <x< 6} 64.{x| 4 < x<5} 65.{x|x<4} 66.{x|x< −2} 67.{x|x> 5} 68.{x|x>−2} 69.(−2,5) ( ) -5 -4 -3 -2 -1 0 1 2 3 4 5 70. (0, 3) ( ) -5 -4 -3 -2 -1 0 1 2 3 4 5 71.[−1, 2] [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 72.[−3, 2] [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 73.(−∞, 3] ] -5 -4 -3 -2 -1 0 1 2 3 4 5 74.(−∞, − 1) ) -5 -4 -3 -2 -1 0 1 2 3 4 5 75.[3, ∞) [ -5 -4 -3 -2 -1 0 1 2 3 4 5 76. [−2, ∞) [ -5 -4 -3 -2 -1 0 1 2 3 4 5 Objective C Exercises 77.AڂB = {1, 2, 4, 6, 9} 78.AڂB = [− 1, 0, 1, 2} 79.AڂB = {2, 3, 5, 8, 9, 10} 80.AڂB = {1, 2, 3, 4, 5, 6, 7, 8} INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .4 Chapter 1 Review of Real Numbers 81.AڂB = {−4, − 2, 0, 2, 4, 8} 82.AڂB = {−3, −2, − 1, 0, 1} 83.AڂB = {1, 2, 3, 4, 5} 84.AڂB = {0, 1, 2, 3, 4, 5} 85.AځB = {6} 86.AځB = {0} 87.AځB = {5, 10, 20} 88.AځB = {1, 9} 89.AځB = ׎ 90.AځB = ׎ 91.AځB = {4, 6} 92.AځB = {− 5, 0, 7} 93.[5, ∞) ځ( 0, 5) 94.{x|x>−1}ڂ{x|x< 6} 95.{x| x> 1} ڂ{x|x< −1} ) ( -5 -4 -3 -2 -1 0 1 2 3 4 5 96.{x| x<2} ڂ{x|x> 4} ] ( -5 -4 -3 -2 -1 0 1 2 3 4 5 97.{x| x<2} ځ{x|x>0} [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 98.{x| x> −1}ځ{x|x<4} ( ] -5 -4 -3 -2 -1 0 1 2 3 4 5 99.{x| x> 1} ځ{x|x>−2} ( -5 -4 -3 -2 -1 0 1 2 3 4 5 100. {x| x< 4}ڂ{x|x<0} ) -5 -4 -3 -2 -1 0 1 2 3 4 5 101. {x| x> −3}ڂ{x|x< 1} -5 -4 -3 -2 -1 0 1 2 3 4 5 102. {x| x> −2}ڂ{x|x< −4} ׎ 103. [−5, 0) ڂ( 1,4] [ ) ( ] -5 -4 -3 -2 -1 0 1 2 3 4 5 104. (−∞,−2] ڂ[3,∞) ] [ -5 -4 -3 -2 -1 0 1 2 3 4 5 105. [−3, 3] ځ [0,5] [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 106. (−∞,1) ځ(−4,∞) ( ) -5 -4 -3 -2 -1 0 1 2 3 4 5 Critical Thinking 107. 4/g31x 108. 5/g116x 109. 51/g100/g16x 110. 77/g116/g16x 111. 22/g31/g14x 112. 23/g33/g14x 113. bax/g33/g16 114. bax/g31/g16NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.2 5 Projects or Group Activities 115. AڂB = A 116. AڂA = A 117. BځB = B 118. AڂC = A 119. AځR = A 120. CځR = C 121. BڂR = R 122. AڂR = R 123. RڂR = R 124. BתC = {0} Section 1.2 Concept Check 1.a) To add two numbers with the same sign add the absolute values of the numbers. Then attach the sign of the addends. b) To add two numbers with different signs find the absolute value of each number. Subtract the smaller of these two numbers from the larger. Then attach the sign of the larger absolute value. 2.To rewrite 8 – (−12) as addition of the opposite value, we change the −12 to its opposite, change the subtraction sign to addition, and rewrite the expression as follows: 8 – (−12) = 8 + 12. 3.No. For example, –5 + ( – 3) = – 8 4.They are both positive or both negative. 5.One number is positive and one number is negative. 6.Yes. For instance, – 3 –(–7) = 4 7.At least one of the numbers is zero. 8.3 7 9.(–5)6 10. 5)28(528 /g152/g16/g31/g152/g16 Objective A Exercises 11.Negative 12.Positive 13.Positive 14.Negative 15. 165)11(15/g32/g16/g16 16. 27 )5( 135 /g16/g32/g16/g121 17.–39– 5 =–39 + ( –5) =–44 18. 22 )6( 16 /g16/g32/g16/g14/g16 19. 29 )3( 87 /g16/g32/g16/g121 20. 25)16( 400 /g32/g16/g121 21. 39–(– 6) = 39 + (6) = 45 22.2 + ( –18) = –16 23.(−12)(15) = –180 24.9–(–29) = 9 + (29) = 38 NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .6 Chapter 1 Review of Real Numbers 25. 14 17 238/g32/g121 26.19– (–13) = 19 + (13) = 32 27.–5 + 19 = 14 28.–9 + ( –11) = –20 29. 11 )4(44 /g16/g32/g16/g121 30.20(–13) = –260 31.–14– 8 =–14 + ( –8) =–22 32.–24(–4) = 96 33.9– (–9) = 9 + (9) =18 34.7(–13) = –91 35.27 + ( –8) = 19 36.15 + ( –16) = –1 37. 2(–26) = –52 38. 19 )21( 399 /g16/g32/g16/g121 39. The total of –6 and 24 is 18. –6 + 24 = 18 40.363 divided by 363 is 1. 1 363 363 /g32/g121 41.80 divided by 80 is 1. 1 8080/g32/g121 42.5 less –27 is 32 5– (–27) = 5 + (27) = 32 43. −56 (−7) = 8 44.–39(–5) = 195 45.–18 + ( –10) = –28 46. 3 )3(9 /g16/g32/g16/g121 47.(–17)(–12) = 204 48. 40 18 720 /g32/g16/g121/g16 49.26 + ( –6) = 20 50.(–3)(15) = –45 51.24–(–2) = 24 + (2) = 26 52.–4– 39 =–4 + ( –39) =–43 53.–21– (–10) =–21 + (10) =–11 54.8–(–9) = 8 + (9) = 17 55.107–(–153) = 107 + (153) 260 The difference between the average temperatures during the day and at night on the moon is 260 oC. 56.–12 + 9 = –3 The temperature at the weather station at 10:00am was –3oF. 57.–282 + 223 = –59 The new elevation of the hiker is –59 ft. 58.The difference in elevation between Salton Sea and Coachella is 148 ft. NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.2 7 Objective B Exercises 59. Negative 60.–45=–1024 (–4)5=–1024 –46=–4096 (–4)6= 4096 (–4)6 is a positive number. 61. 16)2222( 24/g16/g32/g152/g152/g152/g16/g32/g16 62. 81)3333( 34/g16/g32/g152/g152/g152/g16/g32/g16 63. 125 )5()5()5()5(3/g16/g32/g16/g152/g16/g152/g16/g32/g16 64. 2401)7()7()7()7()7(4/g32/g16/g152/g16/g152/g16/g152/g16/g32/g16 65. 1024)2)(2)(2)(2)(2)(2)(2)(2)(2)(2( )2(10 /g32/g16/g16/g16/g16/g16/g16/g16/g16/g16/g16/g32/g16 66. 1024)4)(4)(4)(4)(4()4(5/g16/g32/g16/g16/g16/g16/g16/g32/g16 67.(–1)50= 1 68.–150=–1 69.5– 8 – 12 + 3 = 5 + ( –8) + ( –12) + 3 =–3 + ( –12) + 3 =–15 + 3 =–12 70.48ȉ6 ÷ 3 = 288 ÷ 3 = 96 71.24 ÷ 2ȉ6 = 12ȉ6 = 72 72.14– 4ȉ9 = 14 – 36 = 14 + ( –36) = –22 73.–28– 12 ÷ 4 = –28– 3 = –28 + ( –3) = –31 74.–30 ÷ (2ȉͷሻൌȂ͵ͲൊͳͲൌȂ͵ 75.Ȃͻ൅ͶሺͺȂͳͷሻൌȂͻ൅ͶሺȂ͹ሻൌȂͻ൅ሺȂʹͺሻ ൌȂ͵͹76.ʹሺͷȂ͹ሻȂ͸ሺͳͺȂͶሻ ൌʹሺȂʹሻȂ͸ሺͳͶሻ ൌȂͶȂͺͶ ൌȂͶ൅ሺȂͺͶሻ ൌȂͺͺ 77.ʹ͹ൊሺȂ͵ሻ൅ͷሺʹȂͺሻʹ ൌʹ͹ൊሺȂ͵ሻ൅ͷሺȂ͸ሻʹ ൌʹ͹ൊሺȂ͵ሻ൅ͷሺ͵͸ሻ ൌʹ͹ൊሺȂ͵ሻ൅ͳͺͲ ൌȂͻ൅ͳͺͲ ൌͳ͹ͳ  78.9)96( 133593 /g16/g152/g16/g16 9157464 1326 954 13263 /g16/g16/g16/g32/g16/g16/g16/g32 ) 17496(2/g16/g16/g16/g32  ൌͳ͹ͶͻͶ  79.͵ȉͺȂ͸ሺͶȂͻሻ൅4153/g16 ൌ͵ȉͺȂ͸ሺȂͷሻ൅412/g16ൌʹͶȂሺȂ͵Ͳሻ൅ሺȂ͵ሻ ൌʹͶ൅ሺ͵Ͳሻ൅ሺȂ͵ሻ ൌͷͳ  80.͸͵ൊሺʹȂͷሻʹȉͳ͸ȂͶȉͺȂͳͷ ൌ͸͵ൊሺȂ͵ሻʹȉͳ͸Ȃ 4ȉ8–15 = 63 ÷ 9 ȉ16–4ȉ8–15 = 7ȉ16– 32 – 15 = 112 –32 – 15 = 65 81. –3(5 – 8)3+ (19 – 7) ÷ (1 –3) =–3(–3)3+ (19 – 7) ÷ (1 – 3) =–3(–27) + (12) ÷ ( –2) = 81 + ( –6) = 75 82. 28 ÷ (7 –9)2ȉ(1 –3)4÷ 14 = 28 ÷ ( –2)2ȉ(–2)4 ÷ 14 = 28 ÷ 4 ȉ16 ÷ 14 = 7ȉ16÷14 =112 ÷ 14 =8NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .8 Chapter 1 Review of Real Numbers 83.34 10223 123)72(3 219154 2 2/g152/g16/g152/g152/g121/g16/g152/g16/g152/g16 )48(151296 5)25(3 44/g16/g121/g152/g16/g32/g16/g121/g152/g16/g32  48 15/g16/g121/g16/g32  165/g32  Critical Thinking 84. There is a 3 in the tens place for 1133. 85.There is a 7 in the ones place for 725. 86.The last three digits of 5202 are 625. 87./g11/g12)3(4342 2/g31 Projects or Group Activities 88.a. 7! = 7ȉ6ȉ5ȉ4ȉ3ȉ2ȉ1 = 5040 b. 8!Ȃ6! = (8ȉ7ȉ6ȉ5ȉ4ȉ3ȉ2ȉ1) Ȃሺ6ȉ5ȉ4ȉ3ȉ2ȉ1) = 39,600 c. 0! = 1 d. 504123456123456789 !6!9/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g32 e. 240,301234512345678910 !5!10/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g32 f. 21)12345)(12(1234567 !5!2!7/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g32 g. )!8(!4!12 )!4 12(!4!12/g32/g16 495)12345678)(1234(123456789101112/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g32h. )!3(!8!11 )!811(!8!11/g32/g16 165)123)(12345678(1234567891011/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g32 Section 1.3 Concept Check 1.The least common multiple of two numbers is the smallest number that is a multiple of each of the two numbers. When adding fractions with different denominators we need to first rewrite the fractions as equivalent fractions with a common denominator. The lowest common denominator is the LCM of the denominators. 2.The greatest common factor of two numbers is the largest integer that divides evenly into both numbers. 3.All integers are rational numbers. 4.Answers will vary. An example of two rational numbers that are not integers is –2.34 and 32. 5.There is a smallest possible positive integer. However, there is not a smallest positive rational number. 6.a. The LCM of the denominators 281,85/g16 and 72is 56. b.5635 85/g32 ,562 281/g16/g32/g16 ,5616 72/g32NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.3 9 7.a. The reciprocal of 278/g16 is 827/g16 . b. 49;827 32/g16/g184 /g185/g183/g168 /g169/g167/g16/g152 8.83 41/g121 Objective A Exercises 9.Find the prime factorization of 83 and 2. 83= 83 ȉ1 2 = 2 ȉ1 The LCM = 83 ȉ2 = 166 The GCF is 1. 10. Find the prime factorization of 57 and 9. 57 = 19ȉ3 9 = 3ȉ3 The LCM is 19 ȉ3ȉ3 = 171 The GCF is 3. 11.Find the prime factorization of 15 and 75. 15 = 5ȉ3 75 = 5ȉ5ȉ3 The LCM is 5 ȉ5ȉ3. The GCF is 5 ȉ3 12.Find the prime factorization of 26 and 2. 26 = 13ȉ2 2 = 2ȉ1 The LCM is 26. The GCF is 2. 13.Find the prime factorization of 6 and 2. 6 = 3ȉ2 2 = 2ȉ1 The LCM is 6. The GCF is 2. 14.Find the prime factorization of 110 and 5. 110 = 11ȉ5ȉ2 5 = 5ȉ1 The LCM is 110. The GCF is 5. 15.Find the prime factorization of 10 and 55. 10 = 5ȉ2 55 = 11ȉ5 The LCM is 110. The GCF is 5. 16.Find the prime factorization of 11 and 10. 11 = 11ȉ1 10 = 5ȉ2 The LCM is 110. The GCF is 1. 17.Find the prime factorization of 34 and 85. 34 = 17ȉ2 85 = 17ȉ5 The LCM is 170. The GCF is 17. 18.Find the prime factorization of 96 and 8. 96 = 3ȉ2ȉ2ȉ2ȉ2ȉ2 8 = 2ȉ2ȉ2 The LCM is 96. The GCF is 2. 19.Find the prime factorization of 140 and 7. 140 = 7ȉ5ȉ2ȉ2 7 = 7ȉ1 The LCM is 140. The GCF is 7. 20.Find the prime factorization of 18 and 6. 18 = 3ȉ3ȉ2 6 = 3ȉ2 The LCM is 18. The GCF is 6. 21.Find the prime factorization of 14, 42 and 18. 14 = 7ȉ2 42 = 7ȉ3ȉ2 18 = 3ȉ3ȉ2 The LCM is 126. The GCF is 2. 22.Find the prime factorization of 30, 5 and 6. 30 = 5ȉ3ȉ2 5 = 5ȉ1 6 = 3ȉ2 The LCM is 30. The GCF is 1. NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .10 Chapter 1 Review of Real Numbers 23.Find the prime factorization of 30, 5 and 10. 30 = 5ȉ3ȉ2 5 = 5ȉ1 10 = 5ȉ2 The LCM is 30. The GCF is 5. 24.Find the prime factorization of 4, 27 and 6. 4 = 2ȉ2 27 = 3ȉ3ȉ3 6 = 3ȉ2 The LCM is 108. The GCF is 1. 25.Find the prime factorization of 15, 45 and 10. 15 = 5ȉ3 45 = 5ȉ3ȉ3 10 = 5ȉ2 The LCM is 90. The GCF is 5. 26.Find the prime factorization of 16, 3 and 12. 16 = 2ȉ2ȉ2ȉ2 3 = 3ȉ1 12 = 3ȉ2ȉ2 The LCM is 48. The GCF is 1. 27.Find the prime factorization of 12, 42 and 14. 12 = 3ȉ2ȉ2 42 = 7ȉ3ȉ2 14 = 7ȉ2 The LCM is 84. The GCF is 2. 28.Find the prime factorization of 12, 2 and 14. 12 = 3ȉ2ȉ2 2 = 2ȉ1 14 = 7ȉ2 The LCM is 84. The GCF is 2. Objective B Exercises 29.312435 34 1235 /g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g184 /g185/g183/g168 /g169/g167/g16 935 32232257/g16/g32/g152/g152/g152/g152/g152/g152/g16/g3230.187 2917 21 97/g32/g152/g152/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167/g16 31.29391 299 31 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g184/g185/g183/g168/g169/g167/g16 293 293331/g16/g32/g152/g152/g152/g16/g32 32.21318 21 138 /g152/g152/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167/g16 134 2131222/g32/g152/g152/g152/g152/g32 33.182 1827 91 23 91 23/g14/g16/g32/g14/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16/g16 1825 182 27/g32/g14/g16/g32 34.12253 125 23 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167 85 223253/g16/g32/g152/g152/g152/g152/g16/g32 35.4438 4455 2219 45/g14/g16/g32/g14/g16 4417 4438 55/g16/g32/g14/g16/g32 36.117 1911719 197 1119/g16/g32/g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167 37.14811 18 411 81 411 /g152/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g121/g16 22122 2222211/g32/g32/g152/g152/g152/g152/g32 38.2311 323113 311 233/g32/g152/g152/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167/g16NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.3 11 39.39182 3932 314 3932 /g16/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 1350 39150 39)182( 32/g16/g32/g16/g32/g16/g14/g32 40.207 2015 207 43 207 43/g14/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 1011 2022 207 15/g32/g32/g14/g32 41.274173 2717 43 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167 3617 33322173/g16/g32/g152/g152/g152/g152/g152/g16/g32 42.2825 2880 2825 720/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 415 28105 2825 80/g32/g32/g14/g32 43.394163 3916 43 1639 43 /g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 134 1332222223/g16/g32/g152/g152/g152/g152/g152/g152/g152/g16/g32 44.2628 2613 1314 21/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 2641 2628 13/g32/g14/g32 45.537210 52 3710 25 3710 /g152/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g121/g16 374 537225/g32/g152/g152/g152/g32 46.2278 2277 1139 27/g14/g16/g32/g14/g16 221 2278 77/g32/g14/g16/g3247.9243211 932 2411 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16 2744 3322232222211/g16/g32/g152/g152/g152/g152/g152/g152/g152/g152/g152/g152/g16/g32 48.191 19331 193 31 319 31/g16/g32/g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 49.1136 111312 13 1112 31 1112/g16/g32/g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 50.1518 1513 56 1513/g16/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 1531 1531 151813/g16/g32/g16/g32/g16/g16/g32 51.929 934 95/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 52.3732 3729 373 3729 373/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 53.1817 1811 1828 1811 914/g32/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 54.923 9815 98 915 98 35/g32/g14/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 55.3516 7582 78 52/g32/g152/g152/g32/g184/g185/g183/g168/g169/g167/g16/g16 56.892316 823 916 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16/g184/g185/g183/g168/g169/g167 946 22233232222/g16/g32/g152/g152/g152/g152/g152/g152/g152/g152/g16/g32NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .12 Chapter 1 Review of Real Numbers 57.4039135 4013 395 1340 395 /g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 241 5222133135/g16/g32/g152/g152/g152/g152/g152/g152/g16/g32 58.2120209 2120 209 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16 73 3722522533/g16/g32/g152/g152/g152/g152/g152/g152/g152/g152/g16/g32 59.3664 99 3664 3699 916 411 /g14/g16/g32/g14/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16/g16 3635/g16/g32 60.3315711 337 1511 733 1511 /g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 457 31135711/g16/g32/g152/g152/g152/g152/g16/g32 61.121 1210 129 65 43/g32/g14/g16/g32/g14/g16 62.151 1510 1511 32 1511/g16/g32/g14/g16/g32/g14/g16 63.3659 3626 33 3626 3633 1813 1211/g16/g32/g16/g16/g32/g16/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 64.316815 38 1615 /g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g16 25 3222222235/g16/g32/g152/g152/g152/g152/g152/g152/g152/g152/g16/g32 65.1522 151012 1510 1512 32 54/g16/g32/g16/g16/g32/g16/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 66.181 181516 1815 1816 65 98/g32/g16/g32/g16/g32/g184 /g185/g183/g168 /g169/g167/g1667.5625 7855 75 85 57 85/g16/g32/g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 68.3396 3388 1132 38 /g16/g14/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g14/g16 33184 33184 339688/g16/g32/g16/g32/g16/g16/g32 69.2441 2426 15 2426 2415 1213 85/g32/g14/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g14 70.181 181514 1815 1814 65 97/g32/g14/g16/g32/g14/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g16/g16 71. No. For instance, there is no integer between 2 and 3. 72.Yes. Add the two numbers and divide by 2. Objective C Exercises 73. 85.02017/g32 74. 9375.01615/g32 75. 183.0227/g32 76. 328.06017/g32 77. 641.0125/g32 78. 728.05548/g32 79. 46 461538.0136/g32NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.3 13 80. 90625.03229/g32 81. 34.0 29.0 0986.0 /g32/g121 82. /g11/g12 12.01.2 252.0 /g32/g16/g121/g16 83. 31.3)09.0(4.3 /g32/g16/g14 84. 19.20 20 19.0)20(19.0 /g32/g14/g32/g16/g16 85. 52.3 6.308.0)6.3(08.0 /g16/g32/g16/g32/g16/g14 86. 08.0 )6.1(05.0 /g16/g32/g16 87. 7.58 3.160 )3.1(60 /g16/g32/g14/g16/g32/g16/g16/g16 88. 023.0 027.0 05.0 )027.0( 05.0 /g16/g32/g14/g16/g32/g16/g16/g16 89. 2.5 )4.3(8.1 /g16/g32/g16/g14/g16 90. 045.0 )03.0(5.1 /g16/g32 /g16 91. 8.89 )90(2.0 /g16/g32/g16/g14 92. 035.0 001.0 000035.0 /g32/g16/g121 /g16 93. 756.0)28.0(7.2 /g32/g16/g16 94. 4.0 )03.0( 37.0 /g16/g32/g16/g14/g16 95. 567.36.3 033.0 )6.3( 033.0 /g32/g14/g16/g32/g16/g16/g16 96. 0022.0 15.0 00033.0 /g32/g16/g121 /g16 97. 147.0 017.013.0)017.0(13.0 /g32/g14/g32/g16/g16 98. 004.0 33002.13 /g32/g121 99. /g184 /g185/g183/g168 /g169/g167/g16/g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g121/g161110 58 43 1110 85 43 1112 1110 2024/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g16/g32 100.6445 89 45 21 98 54 21/g16/g32/g152/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g121/g184 /g185/g183/g168 /g169/g167/g16/g121 101.125 61 125 65 322 2 /g16/g184 /g185/g183/g168 /g169/g167/g16/g32/g16/g184 /g185/g183/g168 /g169/g167/g16 187 3614 125 361/g16/g32/g16/g32/g16/g32 102.617 1234 1225 43 45 35 43/g32/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 103.34 65 98 165 43 65 98 165/g152/g16/g152/g16/g32/g121/g16/g152/g16 1825 1820 185/g16/g32/g16/g16/g32 104.85 3617 89 85 43 185 89/g14/g184 /g185/g183/g168 /g169/g167/g16/g16/g32/g14/g184 /g185/g183/g168 /g169/g167/g16/g16 3237 85 3217/g32/g14/g32 105.65 59 32 21 65 95 32 21/g14/g184 /g185/g183/g168 /g169/g167/g152/g16/g32/g14/g184 /g185/g183/g168 /g169/g167/g121/g16 152 304 3025 3615 65 1518 21/g32/g32/g14/g16/g32/g14/g16/g32 106. 2245 432125 85 43/g14/g184 /g185/g183/g168 /g169/g167/g121/g32/g14/g187/g188/g186 /g171/g172/g170/g16/g121 528 510 51825182524 43/g32/g14/g32/g14/g32/g14/g152/g32 107. /g184 /g185/g183/g168 /g169/g167/g16/g16/g32/g184 /g185/g183/g168 /g169/g167/g14/g16/g162413 45 61 241 127 45 61 3227 9681 9665 61/g32/g32/g14/g32 108.53 2429 32 53 65 83 32/g121/g16/g32/g121/g187/g188/g186 /g171/g172/g170/g14/g16 7297 72145 32 35 2429 32/g16/g32/g16/g32/g152/g16/g32NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .14 Chapter 1 Review of Real Numbers 109.32 41 23 213 /g16/g184 /g185/g183/g168 /g169/g167/g16/g16/g121/g184 /g185/g183/g168 /g169/g167/g16 32 47 81 32 47 213 /g16/g16/g121/g16/g32/g16/g184 /g185/g183/g168 /g169/g167/g16/g121/g184 /g185/g183/g168 /g169/g167/g16/g32 4225 32 141 32 74 81/g16/g32/g16/g32/g16/g16/g152/g16/g32 110. /g184 /g185/g183/g168 /g169/g167/g16/g16/g184 /g185/g183/g168 /g169/g167/g16/g121/g184 /g185/g183/g168 /g169/g167/g1632 85 21 54 43 1211 87 /g184 /g185/g183/g168 /g169/g167/g16/g16/g184 /g185/g183/g168 /g169/g167/g16/g121/g16/g32241 21 201 241 /g184 /g185/g183/g168 /g169/g167/g16/g16/g184 /g185/g183/g168 /g169/g167/g16/g152/g16/g32241 21 120 241 4841 481 2420/g32/g14/g32 111. 0.4(1.2 –2.3)2 + 5.8 = 0.4( –1.1)2+ 5.8 = 0.4(1.21) + 5.8 = 6.284 112. 5.4– (0.3)2 ÷ 0.09 = 5.4 –0.09 ÷ 0.09 = 5.4 –1 = 4.4 113. 1.75÷0.25 – (1.25)2 = 1.75÷0.25 –1.5625 = 7 – 1.5625 = 5.4375 114. (3.5 –4.2)2–3.50 ÷ 2.5 = (-0.7)2–3.50 ÷ 2.5 = 0.49 – 1.4 =–0.91 115. 25.76 ÷ (6.54 ÷ 3.27)2 = 25.76 ÷ (2)2 = 25.76 ÷ 4 = 6.44 116. (3.09 – 4.77)2–4.07ȉ3.66 = ( –1.68)2–4.07ȉ3.66 = 2.8224 – 14.8962 =–12.0738 117.65 45 32 54 32 5432 /g32/g152/g32/g121/g32 118.45 23 65 32 65 3265 /g16/g32/g152/g16/g32/g121/g16/g32/g16 119.32 14 61 41 61 4161 21 4365 32 /g16/g32/g152/g16/g32/g121/g16/g32/g16 /g32 /g16/g16 120.21 112 241 121 241 121241 43 32121 81 /g16/g32/g16/g152/g32/g16/g121/g32 /g16/g32 /g16/g16 121. 165125 41 4541 32 43 21 4521 322 /g16/g32 /g184 /g185/g183/g168 /g169/g167/g16/g16 /g32 /g184 /g185/g183/g168 /g169/g167/g16/g184 /g185/g183/g168 /g169/g167/g16 34 516 125 165 125/g16/g32/g16/g152/g32/g16/g121/g32 122. 961517281 125 83121 125 65 8343 323 3 /g16 /g32 /g184 /g185/g183/g168 /g169/g167/g184 /g185/g183/g168 /g169/g167/g16 /g32 /g184 /g185/g183/g168 /g169/g167/g16/g184 /g185/g183/g168 /g169/g167/g16 2701 1596 17281 9615 17281/g16/g32/g152/g16/g32/g121/g16/g32 123.241 1211 85 2411211 85 87 6541 32 85/g16/g121/g16/g32 /g16/g16/g32 /g16/g14 /g16 8181 122 85 124 1211 85/g32/g14/g32/g16/g152/g16/g32NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.3 15 124.67 189 21 67189 21 32 2197 185 21/g121/g16/g14/g32/g16 /g14/g32 /g14/g16 /g14 141 73 21 76 189 21/g32/g16/g14/g32/g152/g16/g14/g32 125.51 5172517 21 51 5342517 21/g14/g16/g32/g14 /g16/g16 51 175 2517 21 51 517 2517 21/g14/g152/g16/g32/g14/g121/g16/g32 21 51 51 21/g32/g14/g16/g32 126.32 65920 43 32 65973 43/g152/g14/g32/g152/g16 /g14 32 56 920 43 32 65 920 43/g152/g152/g14/g32/g152/g121/g14/g32 3691 916 43/g32/g14/g32 127.147 45 14745 153253)45(4321 /g16/g121/g16/g32/g16/g16 /g32 /g16/g152/g152/g16/g16/g152/g16 25 714 45/g32/g16/g152/g16/g32 128.510 89 51089 132)52(31)62(2)52(3 /g121/g16/g32/g16 /g32 /g16/g152/g16/g16/g16/g16/g16 169 105 89/g16/g32/g152/g16/g32Critical Thinking 129. The decimal representation of 235is a rational number since it is the ratio of two integers. Therefore it cannot be a non- terminating, non-repeating decimal. 130. No. By the Order of Operations Agreement, the correct expression to enter is (2/3)(3/4) 131. 3422 32222 122222 /g14/g32 /g16/g14/g32 /g14/g16/g14 27 23243223422 /g32/g14/g32/g152/g14/g32/g121/g14/g32 132. 15654321 87654321 /g14/g14/g14/g32 /g14/g14/g14/g14 15814321 15814321 /g121/g14/g14/g32 /g14/g14/g32 8130321 8130321 8160321 /g121/g14/g32/g14/g32 /g14/g14/g32 101155 30316213038121 /g32/g14/g32/g152/g14/g32 133. 381313 3131313 /g16/g16/g32 /g16/g16/g16 82113 82113 381313 /g121/g16/g32/g16/g32 /g121/g16/g16/g32 2155 218321813 /g32/g16/g32/g152/g16/g32NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .16 Chapter 1 Review of Real Numbers 134. 2211 211 211 211 211 2111 211 211 /g16/g16/g32 /g16/g16/g32 /g16/g16/g16 76 671 32 211 231 211/g32/g32 /g14/g32 /g16/g16/g32 Projects or Group Activities 135. The denominator is the product of a power of 2 and a power of 5. Check Your Progress: Chapter 1 1.{x– 4 < x<5} 2.{x|x> 2} 3.[4, 8] 4.(–∞, – 3) 5.{x| x< –2}ڂ{x| 3 < x<5} ) [ ] -5 -4 -3 -2 -1 0 1 2 3 4 5 6.{x| x< 0} ځ{x|x>–3} [ ) -5 -4 -3 -2 -1 0 1 2 3 4 5 7.–495 ÷ ( –33) = 15 8.–13– 6 = –19 9.9(–15) = –135 10.–6 + ( –30) = –36 11.–28 + ( –10) = –38 12.31 + ( –7) = 24 13.–13– (–17) = –13 + 17 = 4 14.–18 + ( –4) = –22 15.131 13317173 3917 173/g32/g152/g152/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 16.1337 39111 39104 397 38 397/g16/g32/g16/g32/g16/g14/g16/g32/g16/g16 17.1635 1640 165 25 165/g16/g32/g16/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 18. 21836 181 1837/g32/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 19.635 1270 1235 12105 1235 435/g32/g32/g16/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g14 20.923 910 913 910 913/g16/g32/g16/g14/g16/g32/g16/g16 21.2413 244 249 61 83/g32/g14/g32/g184 /g185/g183/g168 /g169/g167/g16/g16 22.35 323235 32 615 23 615/g16/g32/g152/g152/g152/g152/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32/g184 /g185/g183/g168 /g169/g167/g16/g121 23.–5– (–32) = –5 + 32 = 27 24.–2– 3 = –2 + ( –3) = –5 25.–4 + 28 = 24 26.–84 ÷ ( –4) = 21 27.514 522222227 516 87 165 87/g32/g152/g152/g152/g152/g152/g152/g152/g16/g32/g184/g185/g183/g168/g169/g167/g152/g32/g184/g185/g183/g168/g169/g167/g121 28.121 605 6033 6028 2011 157/g16/g32/g16/g32/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g14NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.4 17 29. 691.01211/g32 30. 84375.03227/g32 31.48– 36 ÷ 22= 48 – 36 ÷ 4 = 48 –9 = 39 32.3(4 –7)2–6 ÷ 2ȉ3 = 3(–3)2–3ȉ3 = 3(9) –9 = 27 –9 = 18 33.94 61 43 94 21 31 432 2 /g121/g184 /g185/g183/g168 /g169/g167/g16/g16/g32/g121/g184 /g185/g183/g168 /g169/g167/g16/g16 161 43 49 361 43 94 361 43/g16/g32/g152/g184 /g185/g183/g168 /g169/g167/g16/g32/g121/g184 /g185/g183/g168 /g169/g167/g16/g32 1611 161 1612/g32/g16/g32 34. /g184 /g185/g183/g168 /g169/g167/g16/g121/g32/g184 /g185/g183/g168 /g169/g167/g16/g16/g121155 61 32 65 157 54 61 32 65 181 45 155 61 23 65/g16/g32/g184 /g185/g183/g168 /g169/g167/g16/g152/g32 3643 362 3645/g32/g16/g32 35.161 121 21 161121 21 43 2165 43 21 2/g121/g16/g16/g32/g16 /g16/g32 /g184 /g185/g183/g168 /g169/g167/g16/g16 /g16 611 34 21 116 121 21/g32/g14/g32/g152/g16/g16/g32 Section 1.4 Concept Check 1.Addition and multiplication have a commutative property. 2.Addition and multiplication have an associative property. 3.The inverse of –a is a. 4.The multiplicative inverse of c is c1. 5.Distributive Property 6.Expressions ii and iii are undefined. 7.No. The variable parts are not the same. 8.Yes. They have the same variable part. Objective A Exercises 9. 3443/g152/g32/g152 10.7 + 15 = 15 + 7 11.(3 + 4) + 5 = 3 + (4 + 5) 12. )54(35)43( /g152/g152/g32/g152/g152 13. 05is undefined. 14. 005/g32/g152 15.3(x+ 2) = 3 x+ 6 16.5(y+ 4) = 5 y+ 20 17. 060/g32/g16 18.(x + y ) + [–(x + y )] = 0 19. 11/g32/g152mnmn 20. x x/g32/g1521NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .18 Chapter 1 Review of Real Numbers 21.2(3x) = (2∙3) x 22.ab + bc = bc + ab 23.The Division Property of Zero 24.The Inverse Property of Addition 25.The Inverse Property of Multiplication 26.The Commutative Property of Multiplication 27.The Addition Property of Zero 28.The Associative Property of Addition 29.The Division Property of Zero 30.The Distributive Property 31.The Distributive Property 32.The Multiplication Property of Zero 33.The Associative Property of Multiplication 34.The Commutative Property of Addition 35.When the sum of a positive number nand its additive inverse are multiplied by the reciprocal of the number n, the result is 0. 36.When the product of a negative number nand its reciprocal are multiplied by the number n, the result is n. Objective B Exercises 37.ab + dc 2(3) + (−4)(−1) = 6 + 4 = 10 38.2ab–3dc 2(2)(3) – 3(−4)(−1) = 4(3) – 3(4) = 12 –12 = 0 39.24 a cd/g121 44 164)4)(4(4)4)(1(4 )2()4)(1(42 /g32/g121/g32/g121/g16/g16/g32/g121/g16/g16/g32/g121/g16/g1640. b2–(d– c)2 32– (−4 – (−1))2 = 32– ( −4 + 1)2 = 32–( − 3 )2= 9 – 9 = 0 41.(b–2a)2+ c (3 –2(2))2+ (−1) = (3 – 4)2+ (−1) = (−1)2+ (−1) = 1 + (−1) = 0 42. ) () (2db cb /g16/g121/g16 (3 –(–4))2÷ (3 – (–4)) = (3+4)2 ÷ (3+4) = 72÷ 7 = 49 ÷ 7 = 7 43. 44. 45. 46. 47.71)7(1)7()1()34()23()34()2)1(3() () ( 22 22 /g16/g32/g16/g121/g32/g16/g121/g16/g32/g16/g16/g121/g14/g16/g32/g16/g16/g121/g14/g16/g16/g121/g14 bd a bc 25 169)16(9)64(41)27(31)4(41)3(3141 31 3 33 3 /g32/g14/g32/g16/g16/g32/g16/g16/g32/g16/g16/g16d b 29 214)3(61)16(41)1)(3(61)2(4161 41 44 /g32/g14/g32/g16/g16/g32/g16/g16/g16bc a 29 418)4(1828)9(22)4)(2()3(222 22 /g16/g32/g16/g32/g16/g121/g32/g16/g121/g32/g16/g121/g121adb 21 42 44 4614614)1(614)1)(2(3)1(4)1)(2(343 22 /g32/g32/g16/g32/g16/g16/g16/g32/g16/g16/g16/g32/g16/g16/g16/g32/g16/g16/g16/g16/g16/g16cacNOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONLY USSEE22444444/g32/g32/g32/g32/g16/g16/g32/g32 © Cengage Learning. All Rights Reserved .Section 1.4 19 48. 49. 50. 51. 52.|a2+d| |(2)2+ (−4)| = |4 + (−4)| = |0| = 0 53.–a|a+ 2d| −2|2 + 2( -4)| = −2|2 + (−8)| = −2|−6| = −2(6) = −12 54.d|b –2d| −4|3 – 2(−4)| = −4|3 – (−8)| = −4|3 + 8| = −4|11| = −4(11) = −44 55.56.c bbd 23 /g16/g16 3515 233 12 )1(233)4(3/g16/g32/g16/g32/g14/g16/g16/g32/g16/g16/g16/g16 57.cbc abd/g14/g16/g121/g16243 62 122 1251012164612)1()3(2)1(4)3(2)4(3 /g32/g121/g32/g121/g32/g121/g32/g16/g14/g121/g32/g16/g14/g16/g16/g121/g16/g16 58.c abd bcbc/g16/g14/g14/g162 7161 677616436)1()3(2)4()1(3)1)(3(2 /g32/g14/g32/g16/g14/g32/g16/g14/g32/g14/g16/g16/g14/g32/g16/g16/g16/g14/g16/g14/g16/g16 59. 60.3 2)4( c a d/g121/g16 144 )1( 144)1()12()1()84()1( ))2(44( 3 23 2 3 2 /g16/g32/g16/g121/g32/g16/g121/g16/g32/g16/g121/g16/g16/g32/g16/g121/g16/g16 61. 62.a2c–d3 (2)2(−1) – (−4)3= (4)(−1) – (−64) = −4 + 64 = 60 63.–d3+ 4ac −(−4)3+ 4(2)(−1) = −(−64) + 4(2)(−1) = −(−64) + (8)(−1) = −(−64) + (−8) = 64 + (−8) = 562612 )1(648 )1)(3(2)2(2)4(222 2 /g32/g16/g16/g32/g16/g16/g16/g32/g16/g16/g16/g16 bca d 2714 1614)1(659 )1()2(3)1(5)3(3353 /g32/g32/g14/g32/g16/g16/g14/g32/g16/g16/g16/g16/g16/g16 cacb 2510 2310)2(328 )1(23)2()4(222 /g16/g32/g16/g32/g14/g16/g32/g16/g16/g16/g16/g32/g16/g16/g16/g16/g16/g16 c bad 326 242 )1(3)4(2/g32/g32/g14/g32/g16/g14/g16/g16/g14/g16 cbda 21020 1016419)16(4 )1()3(3)4(4)2(234 2 /g32/g32/g14/g32/g14/g16/g16/g32/g16/g16/g16/g16/g16/g16 cbd a2 7 147)7(2)16()7(2))1(6()7(2))1()2(3()34(2) 3() (2 /g16/g32/g121/g16/g32/g121/g16/g32/g14/g121/g16/g32/g16/g16/g121/g16/g32/g16/g16/g121/g16/g16/g16/g121/g16 ca bd 14 2 16 )2(16)2)(1(16 )2()1()4(3 23 2 /g16/g32/g14/g16/g32/g16/g16/g16/g32/g16/g16/g16/g32/g16/g16/g16/g16/g16/g16 ac dNOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .20 Chapter 1 Review of Real Numbers 64.ba (3)2 = 9 65.)(24a 256 4 44 )2(2/g32/g32 66. ab (2)3 = 8 67.If a= −38, b= −52 and c> 0, the numerator is positive and the denominator is negative therefore, the expression is negative. 68.If a> 20, b = 18 and c < 0, the numerator is negative and the denominator is negative therefore, the expression is positive. Objective C Exercises 69.5x+ 7x = 12 x 70.3x+ 10x= 13x 71.3x– 5x + 9x = 7x 72.−2x + 5x–7x= −4x 73.5b– 8a–12b= −8a–7b 74.−2a + 7b + 9a = 7a+ 7b 75. y y/g32)3(31 76. x x/g32/g184 /g185/g183/g168 /g169/g167 12112 77. z z/g32/g184 /g185/g183/g168 /g169/g167/g16/g1625 52 78.5(x+ 2) = 5 x+ 10 79.3(a– 5) = 3 a–15 80.−3(x– 2) = − 3x+ 6 81.−5(x– 9) = − 5x+ 45 82.–(−x–y) = x + y 83.–(x + y ) = –x–y 84.3(x–2y)–5 = 3 x–6y–5 85.4x–3(2y − 5) = 4 x–6y+ 15 86.3x+ 8(3 x+ 5) = 3 x+ 24x + 40 = 27 x+ 40 87.25x+ 10(9 –x) = 25 x + 90 –10x = 15 x+ 90 88.2x–3(x–2y) = 2 x–3x+ 6y= − x+ 6y 89.3[x–2(x + 2y)] = 3[ x–2x–4y] = 3[− x–4y] = −3 x–12y 90.5 + 2(3 x–7) = 5 + 6 x–14 = 6 x–9 91.7–3(4a–5) = 7 – 12a + 15 = –12a + 22 92.5v–3(2 –4v) = 5 v–6 + 12 v= 17v–6 93.–3m–2(4m+ 3) = –3m–8m–6 =–11m–6 94.–3+ 4(2 z–9) = –3 + 8 z–36 = 8 z– 39 95.–5– 6(2y–3) = –5–12y + 18 = –12y+ 13 96.5[ –2– 6(a– 5)] = 5[ –2– 6a + 30] = 5[28 –6a] = 140 –30a 97.3[a–5(5 –3a)] = 3[ a–25 + 15 a] = 3[16 a–25] = 48 a–75 98. 5[y– 3(y–2x)] = 5[ y–3y + 6x] = 5[6 x–2y] = –10y + 30x 99.−2(x–3y) + 2(3 y– 5x) = −2 x+ 6y + 6y–10x = −12 x + 12 y 100. 4(−a– 2b)–2(3a–5b) = −4 a– 8b– 6a+ 10b = −10 a + 2b NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.5 21 101. 5(3a–2b)– 3(–6a+ 5b) =15 a–10b +18a– 15b = 33 a–25b 102. −7(2 a–b) + 2( –3b+a) = −14 a + 7b–6b+ 2a = −12 a+b 103. 3x–2[y–2(x+ 3[2 x+ 3y])] = 3x–2[y– 2(x + 6x + 9y)] = 3x–2[y– 2(7x+ 9y)] = 3x–2[y– 14x– 18y] = 3x–2[ –14x–17y] = 3 x +28x+ 34y = 31x+ 34y 104. 2x–4[x–4(y–2[5y+ 3])] = 2x–4[x– 4(y–10y– 6)] = 2x–4[x– 4(–9y–6)] = 2x–4[x + 36 y + 24] = 2x–4x–144y–96 = −2 x– 144y–96 105. 4– 2(7x–2y)–3 ( − 2 x+ 3y) = 4 –14x+ 4y+ 6x–9y = 4 –8x–5y 106. 3x+ 8(x–4) –3(2x–y) =3x+ 8x–32 – 6x + 3y = 5x+ 3y–32 107. Simplify 31 a–102b+ 73 –88a + 256 b– 73 to −57 a+ 154 b. a) The coefficient of a is negative. b) The coefficient of b is positive. c) The constant term is 0. 108. The correct answer is (b). Using the Distributive Property we have 3[5 –2(y– 6)] = 15 –6(y– 6) Critical Thinking 109. 0.052 x + 0.072( x+ 1000) = 0.052 x+ 0.072 x+ 72 = 0.124 x+ 72 110. 0.07x+ 0.08(10,000 –x) = 0.07 x+ 800 –0.08x =–0.01x+ 800 111.12 605 602 603 30 20t t t t t t/g32/g32/g14/g32/g14 112.209 204 205 54t t t tt/g32/g14/g32/g14 Projects or Groups Activities 113. a. 654/g32/g133 b. 436/g32/g133 c. 233 32/g32/g133/g32 114. Yes, the operation /g133is commutative. 115. Yes, because 2)53(2 /g32/g133/g133 and /g11/g12 2532 /g32/g133/g133 . 116. Yes, it appears that the operation /g133is associative. 117. The multiplicative inverse of for the /g133operation is 3 because 135/g32/g133 . Section 1.5 Concept Check 1.a. “The sum of aandb” means to addaand b. b. “The product of a and b” means to multiply aandb. c. “The quotient of aand b” means to divide aand b. d. “The diffe rence between aandb” means to subtract aand b. 2.No. The first is x–2; the second is 2 –x. 3.No. The first is m–10; the second is 10 –m. 4.The second number would be expressed as 14–x.NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .22 Chapter 1 Review of Real Numbers Objective A Exercises 5.Let n represent the unknown number. Eight less than a number: n–8 6.Let n represent the unknown number. The product of a negative six and a number: −6n 7.Let n represent the unknown number. Four-fifths of a number : n54 8.Let n represent the unknown number. The difference between a number and twenty: n–20 9.Let n represent the unknown number. The quotient of a number and fourteen: 14n 10.Let n represent the unknown number. A number increased by two hundred: n+ 200 11.Let n represent the unknown number. Five subtracted from the product of the cube of eight and a number: 83n–5 No. This is not the same as the given expression 8 n3– 5. 12.Let n represent the unknown number. Fifteen more than the sum of five times a number and two: (5 n+ 2) + 15. Yes. This is the same as the given expression (5n + 2) + 15. 13.Let n represent the unknown number. A number minus the sum of the number and two: n–(n + 2) n–(n + 2) = n– n– 2 = − 2 14.Let n represent the unknown number. A number decreased bythe difference between five and a number: n–(5 –n) n–(5 –n) = n–5 + n= 2n–515. Let n represent the unknown number. Five times the product of eight and a number: 5(8n) = 40 n 16. Let n represent the unknown number. A number increased bytwo-thirds of the number: n n n35 32/g32/g14 17.Let n represent the unknown number. The difference between seventeen times a number and twice the number: 17n–2n = 15 n 18. Let n represent the unknown number. One-half of the total of six times a number and twenty-two: 113)22 6(21/g14/g32/g14 n n 19. Let n represent the unknown number. The difference between the square of a number and the total of twelve and the square of the number: The square of the number: n 2 The total of twelve and the square of the number: (12 + n2) n2–(12 + n2) =n2–12–n2= −12 20.Let n represent the unknown number. Eleven more than the square of a number added to the difference between the number and seventeen Eleven more than the square of a number: n2+ 11 The difference between the number and seventeen: n–17 (n2+ 11) + ( n–17) = n2+ 11 + n–17 =n2+n–6 21.Let n represent the unknown number. The sum of five times a number and twelve is added to the product of fifteen and the number. Five times the number and twelve: 5 n+ 12 The product of fifteen and the number: 15 n (5n+ 12) + 15 n= 20n + 12 NOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Section 1.5 23 22.Let n represent the unknown number. Four less than twice the sum of a number and eleven. Twice the sum of a number and eleven: 2(n + 11) 2(n + 11) – 4 = 2 n + 22 – 4 = 2 n+ 18 23.The sum of two numbers is fifteen. Let x represent the smaller of the two numbers. The larger number is 15 –x. The sum of two more than the larger number and twice the smaller number: (15 –x+ 2) + 2 x= 17 + x 24.The sum of two numbers is twenty. Let x represent the smalle r of the two numbers. The larger number is 20 –x. The difference between two more than the larger number and twice the smaller number: (20 –x+ 2) –2x = 22 – 3x 25.The sum of two numbers is thirty-four. Let x represent the larger of the two numbers. The smaller number is 34 –x. The quotient of five times the smaller number and the difference between the larger number and three: 3) 34(5 /g16/g16 xx 26.The sum of two numbers is thirty-three. Let x represent the larger of the two numbers. The smaller number is 33 –x. The difference between six more than twice the larger number and the sum of the smaller number and three: (2x+ 6) – (33 –x+ 3) = 2 x + 6 –33 + x– 3 = 3 x–30 Objective B Exercises 27.a) Let j represent the number of jobs in November. December jobs number: j + 200,000 b) Let r represent the unemployment rate in November. December unemployment rate: r– 0.2. 28. Let d represent the number of Internet users. Number of tablet users: t31 29.Let drepresent the distance from Earth to the moon. Distance from the Earth to the sun is 390 times the distance from the Earth to the moon: 390d 30.Let Lrepresent the length of the longest road tunnel in Norway. The longest rail tunnel in Japan is 18.2 mi longer than the longest road tunnel in Norway: L+ 18.2 31. Let xrepresent the amount in the first account. The total amount in both accounts is $10,000. The amount in the second account: 10,000 –x 32. Let L represent the length of the shorter piece. The total length of the board is 12 ft. The length of the longer piece: 12 –L 33.Let x represent the measure of angle B. The measure of angle Ais twice the measure of angle B: 2x The measure of angle C is twice the measure of angle A: 2(2 x) = 4 x 34. Let L represent the length of the longer piece. The total length of the fishing line is 3 ft. The length of the shorter piece: 3 –L 35. In 2013, a house sold for $30,000 less than the same house in sold for in 2010. srepresents the selling price of the house in 2013. 36.In 2013, a house sold for $30,000 less than the same house in sold for in 2010. prepresents the selling price of the house in 2010. NOT FOR SALE INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .24 Chapter 1 Review of Real Numbers Critical Thinking 37. a. The product of mass mand acceleration a: ma b. The product of area A and the square of the velocity v: Av2 c. the sum of the principal P and the interest I: P + I d. the sum of twice the length Land twice the width W: 2L + 2W e. the product of 16 and the time tsquared: 16 t2 f. the product of four- thirds π and the radius r cubed: 3 34r/g83 . g. the quotient of the product of mass 1 mand mass 2 Mand the distance rsquared: 2rmM Projects or Group Activities 38.Answers will vary. For instance, the product of 5 and x; 5 times x. 39.Answers will vary. For instance, the quotient of a and b; the ratio of ato b. 40.The difference between 5 times yand 4. 41.The sum of twice x and 3. 42.5 times the difference between y and 4. 43.Twice the sum of xand 3. Chapter 1 Review Exercises 1.{−2, − 1, 0, 1, 2, 3} 2.AځB = {2, 3} 3.(−2,4] ( ] -5 -4 -3 -2 -1 0 1 2 3 4 5 4.The Associative Property of Multiplication 5.−4.07 + 2.3 = − 1.77 6. 7.−2 ∙ (42) ∙ (-3)2= −2 ∙ 16 ∙ 9 = − 288 8.4y–3[x–2(3 –2x)– 4y] = 4y–3[x– 6 + 4x –4y] = 4y–3[5x–4y– 6] = 4y–15x+ 12y+ 18 = 16 y–15x + 18 9.The additive inverse of 43/g16is 43. 10.{x|x< −3} 11.{x|x< 1} ) -5 -4 -3 -2 -1 0 1 2 3 4 5 12.−10 – (−3) = −10 + 3 = − 7 13. 14.3 + (4 + y) = (3 + 4) + y 15.85 3853 35 83 53 83/g16/g32/g152/g152/g16/g32/g152/g16/g32/g121/g16 16.Replace xwith each element in the set to determine if the inequality is true or false. a)−4 > − 1 False b)−2 > − 1 False c) 0 > − 1 True d) 2 > − 1 True 17.67 1214)12( 14 )12()184())3(4())9(24())3(4())3(24()()2( 22 /g32/g16/g16/g32/g16/g121/g16/g32/g16/g121/g16/g32/g16/g121/g16/g32/g16/g121/g16/g16/g121/g16 ab b a 151 302 3018 203018 3020 53 32 /g16/g32/g16/g32/g14/g16/g32/g14/g16/g32/g14/g16 202 18)2(1836)9(23)2(3)3(232 22 /g32/g14/g32/g16/g16/g32/g16/g16/g32/g16/g16/g16/g16abaNOT FOR SALEfR lN bfR lN b INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .Chapter 1 Review Exercises 25 18.18– |−12 + 8| = 18 – |− 4| = 18 –4 = 14 19. 20. [−3, ∞) [ -5 -4 -3 -2 -1 0 1 2 3 4 5 21.A׫B = {1, 2, 3, 4, 5, 6, 7, 8} 22. 12)17( 204 /g32/g16/g121/g16 23.[x|−2<x< 3} 24.94 32 4161 94 32 43 2165 32 /g121/g16 /g16/g16 /g32/g121/g16 /g16/g16 94 32 41 61/g121/g16/g184 /g185/g183/g168 /g169/g167/g16/g121/g16/g32 49 32 14 61/g152/g16/g184 /g185/g183/g168 /g169/g167/g16/g152/g16/g32 65 23 32/g16/g32/g16/g32 25.6x– 21y= 3(2 x–7y) 26.{x| x<−3} ڂ{x|x> 0} ] ( -5 -4 -3 -2 -1 0 1 2 3 4 5 27.−2(x–3) + 4(2 –x) = − 2x + 6 + 8 – 4x =–6x + 14 28.Replace pwith each element in the set to determine the value of –| p| a) −| −4| = − 4 b) −| 0 | = 0 c) −| 7 | = −7 29.The Inverse Property of Addition 30. 1.3)06.1( 286.3 /g32/g16/g121/g1631. 358.0127/g32 32.Replace ywith each element in the set to determine if the inequality is true or false. a)−4 > − 2 False b)−1 > − 2 True c) 4 > −2 True 33.{−3, −2, − 1, 0, 1} 34.{x| x < 7} 35.A׫B = {−4, − 2, 0, 2, 4, 5, 10} 36.AתB = ׎ 37.{x|x< 3}ת{x|x> −2} ( ] -5 -4 -3 -2 -1 0 1 2 3 4 5 38.(−3,4) ڂ[−1,5] ( ] -5 -4 -3 -2 -1 0 1 2 3 4 5 39.2 – (−3) = 2 + 3 = 5 40. 41.(–3)4– 3(20-1) = ( –3)4– 3(19) =81–57 = 24 42.(−3)3–(2 –6)2∙ 5 = (− 3)3–( −4)2∙5 = −27 – 16 ∙ 5 = – 27– 80 = − 107 43. 44.–(3a+b)–2 ( − 4a–5b) = –3a–b+ 8a+ 10b =5a+ 9b 45. Let x represent the unknown number. Four times the sum of a number and four: 4(x+ 4) = 4 x+ 16 5251320135204949202323202 22 2 /g32/g152/g32/g121/g32/g14/g16/g121/g32/g14/g16/g121 21 63 62 65 31 65/g16/g32/g16/g32/g184/g185/g183/g168/g169/g167/g14/g16/g32/g184/g185/g183/g168/g169/g167/g14/g16 6 4244)3)(1(8 2)3)(1(88 22 /g16/g32/g121/g16/g32/g121/g16/g16/g16/g32/g121/g16/g16/g16/g121/g16 bacNOT FOR SALECh t 1 RCh t 1 R INSTRUCTOR USE ONL Y © Cengage Learning. All Rights Reserved .