Solution Manual for Algebra Foundations: Prealgebra, Introductory Algebra and Intermediate Algebra, 2nd Edition

Chapter 2 Section 2.1 Practice Exercises 1. a. b. If 0 represents the surface of the earth, then 3805 below the surface of the earth is −3805. If zero degrees Fahrenheit is represented by 0°F, then 85 degrees below zero, Fahrenheit is represented by −85°F. 2. 3. a. 0 > −5 since 0 is to the right of −5 on a number line. b. −3 −12 since −7 is to the right of −12 on a number line. 4. a. |−6| = 6 because −6 is 6 units from 0. b. |4| = 4 because 4 is 4 units from 0. c. |−12| = 12 because −12 is 12 units from 0. 5. a. b. The opposite of 14 is −14. The opposite of −9 is −(−9) or 9. 6. a. −|−7| = −7 b. −|4| = −4 c. −(−12) = 12 7. −|x| = −|−6| = −6 8. The planet with the highest average daytime surface temperature is the one that corresponds to the bar that extends the furthest in the positive direction (upward). Venus has the highest average daytime surface temperature. Vocabulary, Readiness & Video Check 2.1 1. The numbers …−3, −2, −1, 0, 1, 2, 3, … are called integers. 2. Positive numbers, negative numbers, and zero together are called signed numbers. 3. The symbols “” are called inequality symbols. 4. Numbers greater than 0 are called positive numbers while numbers less than 0 are called negative numbers. 5. The sign “” means is greater than. 6. On a number line, the greater number is to the right of the lesser number. 7. A number’s distance from 0 on the number line is the number’s absolute value. 8. The numbers −5 and 5 are called opposites. 42 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 9. number of feet a miner works underground 10. The tick marks are labeled with the integers. 11. 0 will always be greater than any of the negative integers. 12. 8; |8| = 8 also. 13. A negative sign can be translated into the phrase “opposite of.” 14. Eyre Exercise Set 2.1 2. If 0 represents the surface of the water, then 25 feet below the surface of the water is −25. 4. If 0 represents sea level, then 282 feet below sea level is −282. 6. If 0 represents 0 degrees Fahrenheit, then 134 degrees above zero is +134. 8. If 0 represents the surface of the ocean, then 14,040 below the surface of the ocean is −14,040. 10. If 0 represents a loss of $0, then a loss of $241 million is −241 million. 12. If 0 represents 0° Celsius, then 10° below 0° Celsius is −10. Since 5° below 0° Celsius is −5 and −10 is less than −5, −10 (or 10° below 0° Celsius) is cooler. 14. From the map, the coldest temperature on record for the state of Arkansas is −29°F. 16. 18. 20. 22. 24. −8 < 0 since −8 is to the left of 0 on a number line. 26. −12 −29 since −27 is to the right of −29 on a number line. 30. 13 > −13 since 13 is to the right of −13 on a number line. 32. |7| = 7 since 7 is 7 units from 0 on a number line. 34. |−19| = 19 since −19 is 19 units from 0 on a number line. 36. |100| = 100 since 100 is 100 units from 0 on a number line. 38. |−10| = 10 since −10 is 10 units from 0 on a number line. Copyright © 2020 Pearson Education, Inc. 43 Chapter 2: Integers and Introduction to Solving Equations ISM: Algebra Foundations 80. −|−8| = −8 −|−4| = −4 Since −8 < −4, −|−8| < −|−4|. 40. The opposite of 8 is negative 8. −(8) = −8 42. The opposite of negative 6 is 6. −(−6) = 6 44. The opposite of 123 is negative 123. −(123) = −123 46. The opposite of negative 13 is 13. −(−13) = 13 48. |−11| = 11 82. −(−38) = 38 Since −22 < 38, −22 −17 since −4 is to the right of −17 on a number line. 72. −|17| = −17 −(−17) = 17 Since −17 < 17, −|17| < −(−17). −|−5|, −(−4), 23 , |10|. 76. −45 0, |−45| > |0|. 1 100. 70. |−8| = 8 |−4| = 4 Since 8 > 4, |−8| > |−4|. 20 + 15 35 104. 14 = 1, −(−3) = 3, −|7| = −7, and |−20| = 20, so the numbers in order from least to greatest are −|7|, 14 , −(−3), |−20|. 106. 33 = 27, −|−11| = −11, −(−10) = 10, −4 = −4, −|2| = −2, so the numbers in order from least to greatest are −|−11|, −4, −|2|, −(−10), and 33. Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations |0| = 0; since 0 4 is false. 9. −54 + 20 = −34 b. |−4| = 4; since 4 = 4, then |−4| > 4 is false. 10. 7 + (−2) = 5 c. |5| = 5; since 5 > 4, then |5| > 4 is true. 11. −3 + 0 = −3 d. |−100| = 100; since 100 > 4, then |−100| > 4 is true. 12. 18 + (−18) = 0 108. a. 13. −64 + 64 = 0 110. (−|−(−7)|) = (−|7|) = −7 112. False; consider 0, where |0| = 0 and 0 is not positive. 114. True; zero is always less than a positive number since it is to the left of it on a number line. 116. No; b > a because b is to the right of a on the number line. 118. answers may vary 14. 6 + (−2) + (−15) = 4 + (−15) = −11 15. 5 + (−3) + 12 + (−14) = 2 + 12 + (−14) = 14 + (−14) =0 16. x + 3y = −6 + 3(2) = −6 + 6 = 0 17. x + y = −13 + (−9) = −22 18. Temperature at 8 a.m. = −7 + (+4) + (+7) = −3 + (+7) =4 The temperature was 4°F at 8 a.m. 120. no; answers may vary Section 2.2 Practice Exercises 1. Calculator Explorations 1. −256 + 97 = −159 2. 811 + (−1058) = −247 2. 3. 6(15) + (−46) = 44 4. −129 + 10(48) = 351 5. −108,650 + (−786,205) = −894,855 3. 6. −196,662 + (−129,856) = −326,518 Vocabulary, Readiness & Video Check 2.2 4. |−3| + |−19| = 3 + 19 = 22 The common sign is negative, so (−3) + (−19) = −22. 5. −12 + (−30) = −42 1. If n is a number, then −n + n = 0. 2. Since x + n = n + x, we say that addition is commutative. 3. If a is a number, then −(−a) = a. 6. 9 + 4 = 13 7. |−1| = 1, |26| = 26, and 26 − 1 = 25 26 > 1, so the answer is positive. −1 + 26 = 25 8. |2| = 2, |−18| = 18, and 18 − 2 = 16 18 > 2, so the answer is negative. 2 + (−18) = −16 4. Since n + (x + a) = (n + x) + a, we say that addition is associative. 5. Negative; the numbers have different signs and the sign of the sum is the same as the sign of the number with the larger absolute value, −6. Copyright © 2020 Pearson Education, Inc. 45 Chapter 2: Integers and Introduction to Solving Equations ISM: Algebra Foundations 6. Negative; the numbers have the same sign⎯both are negative⎯and we keep this common sign in the sum. 7. The diver’s current depth is 231 feet below the surface. Exercise Set 2.2 2. −6 + (−5) = −11 4. 10 + (−3) = 7 6. 9 + (−4) = 5 8. 15 + 42 = 57 10. |−5| + |−4| = 5 + 4 = 9 The common sign is negative, so −5 + (−4) = −9. 12. −62 + 62 = 0 14. |8| − |−3| = 8 − 3 = 5 8 > 3, so the answer is positive. 8 + (−3) = 5 16. −8 + 0 = −8 18. |−9| − |5| = 9 − 5 = 4 9 > 5, so the answer is negative. 5 + (−9) = −4 20. |−6| + |−1| = 6 + 1 = 7 The common sign is negative, so −6 + (−1) = −7. 22. |−23| + |−23| = 23 + 23 = 46 The common sign is negative, so −23 + (−23) = −46. 24. |−400| + |−256| = 400 + 256 = 656 The common sign is negative, so −400 + (−256) = −656. 26. |24| − |−10| = 24 − 10 = 14 24 > 10, so the answer is positive. 24 + (−10) = 14 46 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 28. |−8| − |4| = 8 − 4 = 4 8 > 4, so the answer is negative. −8 + 4 = −4 30. |−89| − |37| = 89 − 37 = 52 89 > 37, so the answer is negative. −89 + 37 = −52 32. |62| − |−32| = 62 − 32 = 30 62 > 32, so the answer is positive. −32 + 62 = 30 34. |−375| − |325| = 375 − 325 = 50 375 > 325, so the answer is negative. 325 + (−375) = −50 36. |−56| + |−33| = 56 + 33 = 89 The common sign is negative, so −56 + (−33) = −89. 38. −1 + 5 + (−8) = 4 + (−8) = −4 40. −103 + (−32) + (−27) = −135 + (−27) = −162 42. 18 + (−9) + 5 + (−2) = 9 + 5 + (−2) = 14 + (−2) = 12 44. 34 + (−12) + (−11) + 213 = 22 + (−11) + 213 = 11 + 213 = 224 46. −12 + (−3) + (−5) = −15 + (−5) = −20 48. −35 + (−12) = −47 68. The sum of −49, −2, and 40 is −49 + (−2) + 40 = −51 + 40 = −11. 70. 0 + (−248) + 8 + (−16) + (−28) + 32 = −248 + 8 + (−16) + (−28) + 32 = −240 + (−16) + (−28) + 32 = −256 + (−28) + 32 = −284 + 32 = −252 The diver’s final depth is 252 meters below the surface. 72. Since −3 (−1)50 since (−1)50 = 1. (−1)55 and (−7)23 are negative since there are an odd number of factors. Note that (−7)23 −10 since 0 is to the right of −10 on a number line. 28. −9(100) = −900 4. −4 < 4 since −4 is to the left of 4 on a number line. 5. −15 −7 since −2 is to the right of −7 on a number line. 7. |−3| = 3 because −3 is 3 units from 0. 8. |−9| = 9 because −9 is 9 units from 0. 29. −12 − 6 − (−6) = −12 + (−6) + 6 = −18 + 6 = −12 30. −4 + (−8) − 16 − (−9) = −4 + (−8) + (−16) + 9 = −12 + (−16) + 9 = −28 + 9 = −19 31. −105 is undefined. 0 32. 7(−16)(0)(−3) = 0 (since one factor is 0) 9. −|−4| = −4 33. Subtract −8 from −12 is −12 − (−8) = −12 + 8 = −4. 10. −(−5) = 5 34. The sum of −17 and −27 is −17 + (−27) = −44. 11. The opposite of 11 is −11. 35. The product of −5 and −25 is −5(−25) = 125. 12. The opposite of −3 is −(−3) = 3. 13. The opposite of 64 is −64. 14. The opposite of 0 is −0 = 0. 36. The quotient of −100 and −5 is 37. Divide a number by −17 is 15. −3 + 15 = 12 16. −9 + (−11) = −20 17. −8(−6)(−1) = 48(−1) = −48 −100 = 20. −5 x or x ÷ (−17). −17 38. The sum of −3 and a number is −3 + x. 39. A number decreased by −18 is x − (−18). Copyright © 2020 Pearson Education, Inc. 53 Chapter 2: Integers and Introduction to Solving Equations 40. The product of −7 and a number is −7 ⋅ x or −7x. 41. x + y = −3 + 12 = 9 42. x − y = −3 − 12 = −3 + (−12) = −15 43. 2y − x = 2(12) − (−3) = 24 − (−3) = 24 + 3 = 27 ISM: Algebra Foundations 10. −4[−6 + 5(−3 + 5)] − 7 = −4[−6 + 5(2)] − 7 = −4[−6 + 10] − 7 = −4(4) − 7 = −16 − 7 = −23 11. x 2 = (−15)2 = (−15)(−15) = 225 44. 3y + x = 3(12) + (−3) = 36 + (−3) = 33 45. 5x = 5(−3) = −15 46. − x 2 = −(−15)2 = −(−15)(−15) = −225 12. 5 y 2 = 5(4) 2 = 5(16) = 80 y 12 = = −4 x −3 5 y 2 = 5(−4)2 = 5(16) = 80 13. x 2 + y = (−6)2 + (−3) = 36 + (−3) = 33 Section 2.5 Practice Exercises 1. (−2)4 = (−2)(−2)(−2)(−2) = 16 14. 4 − x 2 = 4 − (−8)2 = 4 − 64 = −60 2. −24 = −(2)(2)(2)(2) = −16 15. average sum of numbers = number of numbers 17 + (−1) + (−11) + (−13) + (−16) + (−13) + 2 = 7 −35 = 7 = −5 The average of the temperatures is −5°F. 3. 3 ⋅ 62 = 3 ⋅ (6 ⋅ 6) = 3 ⋅ 36 = 108 4. −25 −25 = =5 5(−1) −5 5. −18 + 6 −12 = =3 −3 − 1 −4 Calculator Explorations 3 6. 30 + 50 + (−4) = 30 + 50 + (−64) = 80 + (−64) = 16 1. −120 − 360 = 48 −10 7. −23 + (−4)2 + 15 = −8 + 16 + 1 = 8 + 1 = 9 2. 4750 = −250 −2 + (−17) 8. 2(2 − 9) + (−12) − 3 = 2(−7) + (−12) − 3 = −14 + (−12) − 3 = −26 − 3 = −29 3. −316 + (−458) = −258 28 + (−25) 4. −234 + 86 = 74 −18 + 16 9. (−5) ⋅ −8 + (−3) + 23 = (−5) ⋅ 8 + (−3) + 23 = (−5) ⋅ 8 + (−3) + 8 = −40 + (−3) + 8 = −43 + 8 = −35 Vocabulary, Readiness & Video Check 2.5 1. To simplify −2 ÷ 2 ⋅ (3), which operation should be performed first? division 2. To simplify −9 − 3 ⋅ 4, which operation should be performed first? multiplication 54 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 3. The average of a list of numbers is sum of numbers . number of numbers 26. 7 ⋅ 6 − 6 ⋅ 5 + (−10) = 42 − 6 ⋅ 5 + (−10) = 42 − 30 + (−10) = 12 + (−10) =2 4. To simplify 5[−9 + (−3)] ÷ 4, which operation should be performed first? addition 28. 7 − (−5)2 = 7 − 25 = −18 5. To simplify −2 + 3(10 − 12) ⋅ (−8), which operation should be performed first? subtraction 30. 6. To evaluate x − 3y for x = −7 and y = −1, replace x with −7 and y with −1 and evaluate −7 − 3(−1). 32. 10 ⋅ 53 + 7 = 10 ⋅125 + 7 = 1250 + 7 = 1257 7. A fraction bar means divided by and it is a grouping symbol. 8. To make sure that the entire value of −2, including the sign, is squared. 9. Finding the average is a good application of both order of operations and adding and dividing integers. −3 + 7 ⋅ 7 2 = 4 ⋅ 72 = 4 ⋅ 7 2 = 4 ⋅ 49 = 196 34. 82 − (5 − 2)4 = 82 − 34 = 64 − 81 = −17 36. |12 − 19| ÷ 7 = |−7| ÷ 7 = 7 ÷ 7 = 1 38. −(−2)3 = −(−8) = 8 40. (2 − 7) 2 ÷ (4 − 3) 4 = (−5)2 ÷ 14 = 25 ÷ 1 = 25 2. −24 = −(2)(2)(2)(2) = −16 42. 3 − 15 ⋅ (−4) ÷ (−16) = −12 ⋅ (−4) ÷ (−16) = 12 ⋅ (−4) ÷ (−16) = −48 ÷ (−16) =3 4. (−2)4 = (−2)(−2)(−2)(−2) = 16 44. (−20 − 5) ÷ 5 − 15 = (−25) ÷ 5 − 15 = −5 − 15 = −20 6. 5 ⋅ 23 = 5 ⋅ 8 = 40 46. 3 ⋅ (8 − 3) + (−4) − 10 = 3 ⋅ (5) + (−4) − 10 = 15 + (−4) − 10 = 11 − 10 =1 Exercise Set 2.5 8. 10 − 23 − 12 = −13 − 12 = −25 10. −8 + 4(3) = −8 + 12 = 4 12. 7(−6) + 3 = −42 + 3 = −39 14. −12 + 6 ÷ 3 = −12 + 2 = −10 16. 5 + 9 ⋅ 4 − 20 = 5 + 36 − 20 = 41 − 20 = 21 18. 20 − 15 5 = = −5 −1 −1 20. 88 88 = = −8 −8 − 3 −11 22. 7(−4) − (−6) = −28 + 6 = −22 24. [9 + (−2)]3 = [7]3 = 343 48. (4 − 12) ⋅ (8 − 17) = (−8) ⋅ (−9) = 72 50. (−4 ÷ 4) − (8 ÷ 8) = (−1) − (1) = −2 52. (11 − 32 )3 = (11 − 9)3 = 23 = 8 54. −3(4 − 8)2 + 5(14 − 16)3 = −3(−4)2 + 5(−2)3 = −3(16) + 5(−8) = −48 + (−40) = −88 56. 12 − [7 − (3 − 6)] + (2 − 3)3 = 12 − [7 − (−3)] + (2 − 3)3 = 12 − (7 + 3) + (−1)3 = 12 − 10 + (−1) = 2 + (−1) =1 Copyright © 2020 Pearson Education, Inc. 55 Chapter 2: Integers and Introduction to Solving Equations 58. 10(−1) − (−2)(−3) −10 − 6 = 2[−8 ÷ (−2 − 2)] 2[−8 ÷ (−4)] −16 = 2(2) −16 = 4 = −4 60. −2[6 + 4(2 − 8)] − 25 = −2[6 + 4(−6)] − 25 = −2[6 + (−24)] − 25 = −2(−18) − 25 = 36 − 25 = 11 62. x − y − z = −2 − 4 − (−1) = −2 − 4 + 1 = −6 + 1 = −5 84. The two lowest scores are −14 and −10. −10 − (−14) = −10 + 14 = 4 The difference between the two lowest scores is 4. −14 + (−10) + (−6) −30 = = −10 3 3 The average of the scores is −10. 86. average = 90. 90 ÷ 45 = 2 92. 45 + 90 = 135 94. 3 + 5 + 3 + 5 = 16 The perimeter is 16 centimeters. 66. x 2 + z = (−2)2 + (−1) = 4 + (−1) = 3 96. 17 + 23 + 32 = 72 The perimeter is 72 meters. 98. (7 ⋅ 3 − 4) ⋅ 2 = (21 − 4) ⋅ 2 = 17 ⋅ 2 = 34 4 x 4(−2) −8 = = = −2 68. 4 4 y 100. 2 ⋅ (8 ÷ 4 − 20) = 2 ⋅ (2 − 20) = 2 ⋅ (−18) = −36 102. answers may vary 70. z 2 = (−4)2 = 16 104. answers may vary 2 72. − x = −(−3) = −9 106. (−17)6 = (−17)(−17)(−17)(−17)(−17)(−17) = 24,137,569 74. 3x 2 = 3(−3)2 = 3(9) = 27 76. 3 − z 2 = 3 − (−4)2 = 3 − 16 = −13 78. 3z 2 − x = 3(−4) 2 − (−3) = 3(16) + 3 = 48 + 3 = 51 −18 + (−8) + (−1) + (−1) + 0 + 4 6 −24 = 6 = −4 80. average = 56 −40 + (−20) + (−10) + (−15) + (−5) 5 −90 = 5 = −18 82. average = 88. no; answers may vary 64. 5 x − y + 4 z = 5(−2) − 4 + 4(−1) = −10 − 4 + (−4) = −14 + (−4) = −18 2 ISM: Algebra Foundations 108. 3x 2 + 2 x − y = 3(−18)2 + 2(−18) − 2868 = 3(324) + (−36) − 2868 = 972 + (−36) − 2868 = 936 − 2868 = −1932 110. 5(ab + 3)b = 5(−2 ⋅ 3 + 3)3 Copyright © 2020 Pearson Education, Inc. = 5(−6 + 3)3 = 5(−3)3 = 5(−27) = −135 ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 7. Section 2.6 Practice Exercises 1. −4 x − 3 = 5 −4(−2) − 3 ⱨ 5 8−3ⱨ 5 5 = 5 True Since 5 = 5 is true, −2 is a solution of the equation. 2. y − 6 = −2 y − 6 + 6 = −2 + 6 y=4 Check: y − 6 = −2 4−6ⱨ −2 −2 = −2 True The solution is 4. 3. −2 = z + 8 −2 − 8 = z + 8 − 8 −10 = z Check: −2 = z + 8 −2 ⱨ − 10 + 8 −2 = −2 True The solution is −10. 4. x = −2 + 90 + (−100) x = 88 + (−100) x = −12 The solution is −12. 5. 3 y = −18 3 y −18 = 3 3 3 −18 ⋅y= 3 3 y = −6 Check: 3 y = −18 3(−6) ⱨ − 18 −18 = −18 True The solution is −6. 6. −32 = 8 x −32 8 x = 8 8 −32 8 = ⋅x 8 8 −4 = x Check: −32 = 8 x −32 ⱨ 8(−4) −32 = −32 True The solution is −4. 8. −3 y = −27 −3 y −27 = −3 −3 −3 −27 ⋅y= −3 −3 y=9 Check: −3 y = −27 −3 ⋅ 9 ⱨ − 27 −27 = −27 True The solution is 9. x =7 −4 x −4 ⋅ = −4 ⋅ 7 −4 −4 ⋅ x = −4 ⋅ 7 −4 x = −28 x =7 Check: −4 −28 ⱨ7 −4 7 = 7 True The solution is −28. Vocabulary, Readiness & Video Check 2.6 1. A combination of operations on variables and numbers is called an expression. 2. A statement of the form “expression = expression” is called an equation. 3. An equation contains an equal sign (=) while an expression does not. 4. An expression may be simplified and evaluated while an equation may be solved. 5. A solution of an equation is a number that when substituted for the variable makes the equation a true statement. 6. Equivalent equations have the same solution. 7. By the addition property of equality, the same number may be added to or subtracted from both sides of an equation without changing the solution of the equation. 8. By the multiplication property of equality, both sides of an equation may be multiplied or divided by the same nonzero number without changing the solution of the equation. Copyright © 2020 Pearson Education, Inc. 57 Chapter 2: Integers and Introduction to Solving Equations 9. an equal sign ISM: Algebra Foundations 12. s − 7 = −15 s − 7 + 7 = −15 + 7 s = −8 Check: s − 7 = −15 −8 − 7 ⱨ − 15 −15 = −15 True The solution is −8. 14. 1= y+7 1− 7 = y + 7 − 7 −6 = y Check: 1 = y + 7 1ⱨ −6+ 7 1 = 1 True The solution is −6. 10. We can add the same number to both sides of an equation and we’ll have an equivalent equation. Also, we can subtract the same number from both sides of an equation and have an equivalent equation. 11. To check a solution, we go back to the original equation, replace the variable with the proposed solution, and see if we get a true statement. Exercise Set 2.6 2. y − 16 = −7 9 − 16 ⱨ − 7 −7 = −7 True Since −7 = −7 is true, 9 is a solution of the equation. 4. a + 23 = −16 −7 + 23 ⱨ − 16 16 = −16 False Since 16 = −16 is false, −7 is not a solution of the equation. 6. −3k = 12 − k −3(−6) ⱨ 12 − (−6) 18 ⱨ 12 + 6 18 = 18 True Since 18 = 18 is true, −6 is a solution of the equation. 8. 2(b − 3) = 10 2(1 − 3) ⱨ 10 2(−2) ⱨ 10 −4 = 10 False Since −4 = 10 is false, 1 is not a solution of the equation. 10. f + 4 = −6 f + 4 − 4 = −6 − 4 f = −10 f + 4 = −6 −10 + 4 ⱨ − 6 −6 = −6 True The solution is −10. Check: 58 16. −50 + 40 − 5 = z −10 − 5 = z −15 = z Check: −50 + 40 − 5 = z −50 + 40 − 5 ⱨ − 15 −10 − 5 ⱨ − 15 −15 = −15 True The solution is −15. 18. 6 y = 48 6 y 48 = 6 6 6 48 ⋅y= 6 6 y =8 Check: 6 y = 48 6(8) ⱨ 48 48 = 48 True The solution is 8. 20. −2 x = 26 −2 x 26 = −2 −2 −2 26 ⋅x = −2 −2 x = −13 Check: −2 x = 26 −2(−13) ⱨ 26 26 = 26 True The solution is −13. Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations 22. 24. 26. 28. n = −5 11 n 11 ⋅ = 11 ⋅ (−5) 11 11 ⋅ n = 11 ⋅ (−5) 11 n = −55 n = −5 Check: 11 −55 ⱨ −5 11 −5 = −5 True The solution is −55. 7 y = −21 7 y −21 = 7 7 7 −21 ⋅y= 7 7 y = −3 Check: 7 y = −21 7 ⋅ (−3) ⱨ − 21 −21 = −21 True The solution is −3. −9 x = 0 −9 x 0 = −9 −9 −9 0 ⋅x = −9 −9 x=0 Check: −9 x = 0 −9 ⋅ 0 ⱨ 0 0 = 0 True The solution is 0. −31x = −31 −31x −31 = −31 −31 −31 −31 ⋅x = −31 −31 x =1 Check: −31x = −31 −31 ⋅1 ⱨ − 31 −31 = −31 True The solution is 1. Chapter 2: Integers and Introduction to Solving Equations 30. 3 y = −27 3 y −27 = 3 3 3 −27 ⋅y= 3 3 y = −9 The solution is −9. 32. n − 4 = −48 n − 4 + 4 = −48 + 4 n = −44 The solution is −44. 34. −36 = y + 12 −36 − 12 = y + 12 − 12 −48 = y The solution is −48. 36. x = −9 −9 x −9 ⋅ = −9 ⋅ (−9) −9 −9 ⋅ x = −9 ⋅ (−9) −9 x = 81 The solution is 81. 38. z = −28 + 36 z=8 The solution is 8. 40. 42. −11x = −121 −11x −121 = −11 −11 −11 −121 ⋅x = −11 −11 x = 11 The solution is 11. n = −20 5 n 5 ⋅ = 5 ⋅ (−20) 5 5 ⋅ n = 5 ⋅ (−20) 5 n = −100 The solution is −100. Copyright © 2020 Pearson Education, Inc. 59 Chapter 2: Integers and Introduction to Solving Equations ISM: Algebra Foundations 44. −81 = 27 x −81 27 x = 27 27 −81 27 = ⋅x 27 27 −3 = x The solution is −3. 46. A number increased by −5 is x + (−5). 48. The quotient of a number and −20 is x ÷ (−20) or x . −20 50. −32 multiplied by a number is −32 ⋅ x or −32x. 52. Subtract a number from −18 is −18 − x. 54. 56. n + 961 = 120 n + 961 − 961 = 120 − 961 n = −841 The solution is −841. y = 1098 −18 y −18 ⋅ = −18 ⋅1098 −18 −18 ⋅ y = −18 ⋅1098 −18 y = −19, 764 The solution is −19,764. 58. answers may vary 60. answers may vary Chapter 2 Vocabulary Check 1. Two numbers that are the same distance from 0 on the number line but are on opposite sides of 0 are called opposites. 2. The absolute value of a number is that number’s distance from 0 on a number line. 3. The integers are …, −3, −2, −1, 0, 1, 2, 3, …. 4. The negative numbers are numbers less than zero. 5. The positive numbers are numbers greater than zero. 6. The symbols “” are called inequality symbols. 7. A solution of an equation is a number that when substituted for the variable makes the equation a true statement. 8. The average of a list of numbers is 60 sum of numbers . number of numbers Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 9. A combination of operations on variables and numbers is called an expression. 10. A statement of the form “expression = expression” is called an equation. 11. The sign “” means is greater than. 12. By the addition property of equality, the same number may be added to or subtracted from both sides of an equation without changing the solution of the equation. 13. By the multiplication property of equality, both sides of an equation may be multiplied or divided by the same nonzero number without changing the solution of the equation. Chapter 2 Review 1. If 0 represents ground level, then 1572 feet below the ground is −1572. 2. If 0 represents sea level, then an elevation of 11,239 feet is +11,239. 3. 4. 5. |−11| = 11 since −11 is 11 units from 0 on a number line. 6. |0| = 0 since 0 is 0 units from 0 on a number line. 7. −|8| = −8 8. −(−9) = 9 9. −|−16| = −16 10. −(−2) = 2 11. −18 > −20 since −18 is to the right of −20 on a number line. 12. −5 −198, |−123| > −|−198|. 14. |−12| = 12 −|−16| = −16 Since 12 > −16, |−12| > −|−16|. 15. The opposite of −18 is 18. −(−18) = 18 16. The opposite of 42 is negative 42. −(42) = −42 17. False; consider a = 1 and b = 2, then 1 3, so the answer is positive. 5 + (−3) = 2 28. |18| − |−4| = 18 − 4 = 14 18 > 4, so the answer is positive. 18 + (−4) = 14 43. 12 − 4 = 12 + (−4) = 8 44. −12 − 4 = −12 + (−4) = −16 45. −7 − 17 = −7 + (−17) = −24 29. |16| − |−12| = 16 − 12 = 4 16 > 12, so the answer is positive. −12 + 16 = 4 46. 7 − 17 = 7 + (−17) = −10 30. |40| − |−23| = 40 − 23 = 17 40 > 23, so the answer is positive. −23 + 40 = 17 48. −6 − (−14) = −6 + 14 = 8 47. 7 − (−13) = 7 + 13 = 20 49. 16 − 16 = 16 + (−16) = 0 31. |−8| + |−15| = 8 + 15 = 23 The common sign is negative, so −8 + (−15) = −23. 50. −16 − 16 = −16 + (−16) = −32 32. |−5| + |−17| = 5 + 17 = 22 The common sign is negative, so −5 + (−17) = −22. 52. −5 − (−12) = −5 + 12 = 7 33. |−24| − |3| = 24 − 3 = 21 24 > 3, so the answer is negative. −24 + 3 = −21 34. |−89| − |19| = 89 − 19 = 70 89 > 19, so the answer is negative. −89 + 19 = −70 35. 15 + (−15) = 0 51. −12 − (−12) = −12 + 12 = 0 53. −(−5) − 12 + (−3) = 5 + (−12) + (−3) = −7 + (−3) = −10 54. −8 + (−12) − 10 − (−3) = −8 + (−12) + (−10) + 3 = −20 + (−10) + 3 = −30 + 3 = −27 55. 600 − (−92) = 600 + 92 = 692 The difference in elevations is 692 feet. 36. −24 + 24 = 0 62 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 56. 142 − 125 + 43 − 85 = 142 + (−125) + 43 + (−85) = 17 + 43 + (−85) = 60 + (−85) = −25 The balance in his account is −25. 74. −72 = −9 8 75. −38 = 38 −1 57. 85 − 99 = 85 + (−99) = −14 You are −14 feet or 14 feet below ground at the end of the drop. 76. 45 = −5 −9 58. 66 − (−16) = 66 + 16 = 82 The total length of the elevator shaft for Elevator C is 82 feet. 77. A loss of 5 yards is represented by −5. (−5)(2) = −10 The total loss is 10 yards. 59. |−5| − |−6| = 5 − 6 = 5 + (−6) = −1 5 − 6 = 5 + (−6) = −1 |−5| − |−6| = 5 − 6 is true. 78. A loss of $50 is represented by −50. (−50)(4) = −200 The total loss is $200. 60. |−5 − (−6)| = |−5 + 6| = |1| = 1 5 + 6 = 11 Since 1 ≠ 11, the statement is false. 79. A debt of $1024 is represented by −1024. −1024 ÷ 4 = −256 Each payment is $256. 61. −3(−7) = 21 80. A drop of 45 degrees is represented by −45. −45 = −5 or −45 ÷ 9 = −5 9 The average drop each hour is 5°F. 62. −6(3) = −18 63. −4(16) = −64 81. (−7)2 = (−7)(−7) = 49 64. −5(−12) = 60 82. −72 = −(7 ⋅ 7) = −49 65. (−5)2 = (−5)(−5) = 25 66. (−1)5 = (−1)(−1)(−1)(−1)(−1) = −1 84. −3 + 12 + (−7) − 10 = 9 + (−7) − 10 = 2 − 10 = −8 67. 12(−3)(0) = 0 68. −1(6)(2)(−2) = −6(2)(−2) = −12(−2) = 24 69. −15 ÷ 3 = −5 70. −24 =3 −8 71. 0 =0 −3 72. −46 is undefined. 0 73. 100 = −20 −5 83. 5 − 8 + 3 = −3 + 3 = 0 85. −10 + 3 ⋅ (−2) = −10 + (−6) = −16 86. 5 − 10 ⋅ (−3) = 5 − (−30) = 5 + 30 = 35 87. 16 ÷ (−2) ⋅ 4 = −8 ⋅ 4 = −32 88. −20 ÷ 5 ⋅ 2 = −4 ⋅ 2 = −8 89. 16 + (−3) ⋅12 ÷ 4 = 16 + (−36) ÷ 4 = 16 + (−9) =7 90. −12 + 10 ÷ (−5) = −12 + (−2) = −14 91. 43 − (8 − 3)2 = 43 − (5)2 = 64 − 25 = 39 92. (−3)3 − 90 = −27 − 90 = −117 Copyright © 2020 Pearson Education, Inc. 63 Chapter 2: Integers and Introduction to Solving Equations 93. (−4)(−3) − (−2)(−1) 12 − 2 10 = = = −2 −10 + 5 −5 −5 94. 4(12 − 18) 4(−6) −24 = = = −12 −10 ÷ (−2 − 3) −10 ÷ (−5) 2 −18 + 25 + (−30) + 7 + 0 + (−2) 6 −18 = 6 = −3 95. average = −45 + (−40) + (−30) + (−25) 4 −140 = 4 = −35 ISM: Algebra Foundations 105. 10 x = −30 10 x −30 = 10 10 10 −30 ⋅x = 10 10 x = −3 The solution is −3. 106. −8 x = 72 −8 x 72 = −8 −8 72 −8 ⋅x = −8 −8 x = −9 The solution is −9. 96. average = 97. 2x − y = 2(−2) − 1 = −4 − 1 = −5 108. 98. y 2 + x 2 = 12 + (−2)2 = 1 + 4 = 5 99. 3 x 3(−2) −6 = = = −1 6 6 6 5 y − x 5(1) − (−2) 5 + 2 7 = = = = −7 100. −y −1 −1 −1 101. 107. −20 + 7 = y −13 = y The solution is −13. 2n − 6 = 16 2(−5) − 6 ⱨ 16 −10 − 6 ⱨ 16 −16 = 16 False Since −16 = 16 is false, −5 is not a solution of the equation. 109. 110. x − 31 = −62 x − 31 + 31 = −62 + 31 x = −31 The solution is −31. n = −11 −4 n −4 ⋅ = −4 ⋅ (−11) −4 −4 ⋅ n = −4 ⋅ (−11) −4 n = 44 The solution is 44. x = 13 −2 x −2 ⋅ = −2 ⋅13 −2 −2 ⋅ x = −2 ⋅13 −2 x = −26 The solution is −26. 102. 2(c − 8) = −20 2(−2 − 8) ⱨ − 20 2(−10) ⱨ − 20 −20 = −20 True Since −20 = −20 is true, −2 is a solution of the equation. 103. n − 7 = −20 n − 7 + 7 = −20 + 7 n = −13 The solution is −13. 111. n + 12 = −7 n + 12 − 12 = −7 − 12 n = −19 The solution is −19. 104. −5 = n + 15 −5 − 15 = n + 15 − 15 −20 = n The solution is −20. 112. n − 40 = −2 n − 40 + 40 = −2 + 40 n = 38 The solution is 38. 64 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 113. −36 = −6 x −36 −6 x = −6 −6 −36 −6 = ⋅x −6 −6 6= x The solution is 6. 129. 7 + 2(−3) = −14 − 6 −20 = = −20 7 + (−6) 1 130. 5(7 − 6)3 − 4(2 − 3)2 + 24 = 5(1)3 − 4(−1)2 + 24 = 5(1) − 4(1) + 16 = 5 − 4 + 16 = 1 + 16 = 17 114. −40 = 8 y −40 8 y = 8 8 −40 8 = ⋅y 8 8 −5 = y The solution is −5. 131. n − 9 = −30 n − 9 + 9 = −30 + 9 n = −21 The solution is −21. 132. n + 18 = 1 n + 18 − 18 = 1 − 18 n = −17 The solution is −17. 133. −4 x = −48 −4 x −48 = −4 −4 −4 −48 ⋅x = −4 −4 x = 12 The solution is 12. 134. 9 x = −81 9 x −81 = 9 9 −81 9 ⋅x = 9 9 x = −9 The solution is −9. 115. −6 + (−9) = −15 116. −16 − 3 = −16 + (−3) = −19 117. −4(−12) = 48 118. − −14 − 6 84 = −21 −4 119. −76 − (−97) = −76 + 97 = 21 120. −9 + 4 = −5 121. −18 − 9 = −27 The temperature on Friday was −27°C. 122. −11 + 17 = 6 The temperature at noon on Tuesday was 6°C. 123. 12,923 − (−195) = 12,923 + 195 = 13,118 The difference in elevations is 13,118 feet. 124. −32 + 23 = −9 His financial situation can be represented by −9. 125. (3 − 7)2 ÷ (6 − 4)3 = (−4)2 ÷ (2)3 = 16 ÷ 8 = 2 126. 3(4 + 2) + (−6) − 32 = 3(6) + (−6) − 32 = 3(6) + (−6) − 9 = 18 + (−6) − 9 = 12 − 9 =3 135. n = 100 −2 n −2 ⋅ = −2 ⋅100 −2 −2 ⋅ n = −2 ⋅100 −2 n = −200 The solution is −200. 127. 2 − 4 ⋅ 3 + 5 = 2 − 12 + 5 = −10 + 5 = −5 128. 4 − 6 ⋅ 5 + 1 = 4 − 30 + 1 = −26 + 1 = −25 Copyright © 2020 Pearson Education, Inc. 65 Chapter 2: Integers and Introduction to Solving Equations 136. y = −3 −1 y −1 ⋅ = −1(−3) −1 −1 ⋅ y = −1 ⋅ (−3) −1 y=3 The solution is 3. ISM: Algebra Foundations 13. 14. Chapter 2 Getting Ready For the Test 1. The opposite of −2 is −(−2) = 2; A. 2. The absolute value of −2 is |−2| = 2 because −2 is 2 units from 0 on a number line; A. 3. The absolute value of 2 is |2| = 2 because 2 is 2 units from 0 on a number line; A. 5. For xy, the operation is multiplication; C. 6. For −12(+3), the operation is multiplication; C. 7. For −12 + 3, the operation is addition; A. −12 , the operation is division; D. 8. For +3 9. For 4 + 6 ⋅ 2, the operation of multiplication is performed first, since multiplication and division are performed before addition and subtraction; C. 10. For 4 + 6 ÷ 2, the operation of division is performed first, since multiplication and division are performed before addition and subtraction; D. 12. x − 2 = −4 x − 2 + 2 = −4 + 2 x = −2 Choice B is correct. x+2 = 4 x+2−2 = 4−2 x=2 Choice A is correct. Chapter 2 Test 1. −5 + 8 = 3 2. 18 − 24 = 18 + (−24) = −6 3. 5 ⋅ (−20) = −100 4. The opposite of 2 is −2; B. 11. −3x = 6 −3 x 6 = −3 −3 x = −2 Choice B is correct. x =6 −3 ⎛ x ⎞ −3 ⎜ ⎟ = −3(6) ⎝ −3 ⎠ x = −18 Choice D is correct. 4. −16 ÷ (−4) = 4 5. −18 + (−12) = −30 6. −7 − (−19) = −7 + 19 = 12 7. −5 ⋅ (−13) = 65 8. −25 =5 −5 9. |−25| + (−13) = 25 + (−13) = 12 10. 14 − |−20| = 14 − 20 = 14 + (−20) = −6 11. |5| ⋅ |−10| = 5 ⋅ 10 = 50 12. −10 − −5 = 10 = −2 −5 13. −8 + 9 ÷ (−3) = −8 + (−3) = −11 14. −7 + (−32) − 12 + 5 = −7 + (−32) + (−12) + 5 = −39 + (−12) + 5 = −51 + 5 = −46 15. (−5)3 − 24 ÷ (−3) = −125 − 24 ÷ (−3) = −125 − (−8) = −125 + 8 = −117 16. (5 − 9)2 ⋅ (8 − 2)3 = (−4) 2 ⋅ (6)3 = 16 ⋅ 216 = 3456 66 Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations Chapter 2: Integers and Introduction to Solving Equations 17. −(−7)2 ÷ 7 ⋅ (−4) = −49 ÷ 7 ⋅ (−4) = −7 ⋅ (−4) = 28 18. 3 − (8 − 2)3 = 3 − 63 = 3 − 216 = 3 + (−216) = −213 29. Subtract the depth of the lake from the elevation of the surface. 1495 − 5315 = 1495 + (−5315) = −3820 The deepest point of the lake is 3820 feet below sea level. 30. average = 19. 4 82 4 64 − = − = 2 − 4 = 2 + (−4) = −2 2 16 2 16 20. −3(−2) + 12 6 + 12 18 = = =2 −1(−4 − 5) −1(−9) 9 31. a. b. 32. 21. 25 − 30 2 2(−6) + 7 = −5 2 −12 + 7 = 2 (5) 25 = = −5 −5 −5 22. 5(−8) − [6 − (2 − 4)] + (12 − 16) 2 = 5(−8) − [6 − (−2)] + (12 − 16)2 = 5(−8) − (6 + 2) + (−4)2 33. = 5(−8) − 8 + (−4)2 = 5(−8) − 8 + 16 = −40 − 8 + 16 = −48 + 16 = −32 23. 7 x + 3 y − 4 z = 7(0) + 3(−3) − 4(2) = 0 + (−9) − 8 = −9 − 8 = −17 24. 10 − y 2 = 10 − (−3)2 = 10 − 9 = 1 25. 3z 3(2) 6 = = = −1 2 y 2(−3) −6 26. A descent of 22 feet is represented by −22. 4(−22) = −88 Mary is 88 feet below sea level. 27. 129 + (−79) + (−40) + 35 = 50 + (−40) + 35 = 10 + 35 = 45 His new balance can be represented by 45. 34. −12 + (−13) + 0 + 9 −16 = = −4 4 4 The product of a number and 17 is 17 ⋅ x or 17x. A number subtracted from 20 is 20 − x. −9n = −45 −9n −45 = −9 −9 −9 −45 ⋅n = −9 −9 n=5 The solution is 5. n =4 −7 n −7 ⋅ = −7 ⋅ 4 −7 −7 ⋅ n = −7 ⋅ 4 −7 n = −28 The solution is −28. x − 16 = −36 x − 16 + 16 = −36 + 16 x = −20 The solution is −20. 35. −20 + 8 + 8 = x −12 + 8 = x −4 = x The solution is −4. Cumulative Review Chapters 1−2 1. The place value of 3 in 396,418 is hundredthousands. 2. The place value of 3 in 4308 is hundreds. 3. The place value of 3 in 93,192 is thousands. 28. Subtract the elevation of the Romanche Gap from the elevation of Mt. Washington. 6288 − (−25,354) = 6288 + 25,354 = 31,642 The difference in elevations is 31,642 feet. 4. The place value of 3 is 693,298 is thousands. 5. The place value of 3 in 534,275,866 is tenmillions. Copyright © 2020 Pearson Education, Inc. 67 Chapter 2: Integers and Introduction to Solving Equations 6. The place value of 3 in 267,301,818 is hundredthousands. 7. a. −7 −4 since 0 is to the right of −4 on a number line. c. −9 > −11 since −9 is to the right of −11 on a number line. 8. a. 12 > −4 since 12 is to the right of −4 on a number line. b. −13 > −31 since −13 is to the right of −31 on a number line. c. −82 < 79 since −82 is to the left of 79 on a number line. 9. 13 + 2 + 7 + 8 + 9 = (13 + 7) + (2 + 8) + 9 = 20 + 10 + 9 = 39 ISM: Algebra Foundations 15. To round 568 to the nearest ten, observe that the digit in the ones place is 8. Since this digit is at least 5, we add 1 to the digit in the tens place. The number 568 rounded to the nearest ten is 570. 16. To round 568 to the nearest hundred, observe that the digit in the tens place is 6. Since this digit is at least 5, we add 1 to the digit in the hundreds place. The number 568 rounded to the nearest hundred is 600. 17. 4725 − 2879 rounds to rounds to 4700 − 2900 1800 18. 8394 − 2913 rounds to rounds to 8000 − 3000 5000 19. a. 10. 11 + 3 + 9 + 16 = (11 + 9) + (3 + 16) = 20 + 19 = 39 11. 12. 7826 − 505 7321 Check: 3285 − 272 3013 Check: b. 20(4 + 7) = 20 ⋅ 4 + 20 ⋅ 7 c. 2(7 + 9) = 2 ⋅ 7 + 2 ⋅ 9 20. a. 7321 + 505 7826 3013 + 272 3285 13. Subtract 7257 from the radius of Jupiter. 43, 441 − 7 257 36,184 The radius of Saturn is 36,184 miles. 68 5(2 + 12) = 5 ⋅ 2 + 5 ⋅ 12 b. 9(3 + 6) = 9 ⋅ 3 + 9 ⋅ 6 c. 4(8 + 1) = 4 ⋅ 8 + 4 ⋅ 1 21. 631 × 125 3 155 12 620 63 100 78,875 22. 299 × 104 1 196 29 900 31, 096 23. a. 14. Subtract the cost of the camera from the amount in her account. 762 − 237 525 She will have $525 left in her account after buying the camera. 5(6 + 5) = 5 ⋅ 6 + 5 ⋅ 5 b. c. 42 ÷ 7 = 6 because 6 ⋅ 7 = 42. 64 = 8 because 8 ⋅ 8 = 64. 8 7 3 21 because 7 ⋅ 3 = 21. Copyright © 2020 Pearson Education, Inc. ISM: Algebra Foundations 24. a. Chapter 2: Integers and Introduction to Solving Equations 35 = 7 because 7 ⋅ 5 = 35. 5 28. b. 64 ÷ 8 = 8 because 8 ⋅ 8 = 64. c. 12 4 48 because 12 ⋅ 4 = 48. 741 25. 5 3705 −35 20 −20 05 −5 0 Check: 741 × 5 3705 Cost of each total = ÷ number of tickets ticket cost = 324 ÷ 36 9 36 324 −324 0 Each ticket cost $9. 29. 92 = 9 ⋅ 9 = 81 30. 53 = 5 ⋅ 5 ⋅ 5 = 125 31. 61 = 6 32. 41 = 4 33. 5 ⋅ 62 = 5 ⋅ 6 ⋅ 6 = 180 34. 23 ⋅ 7 = 2 ⋅ 2 ⋅ 2 ⋅ 7 = 56 456 26. 8 3648 −32 44 −40 48 −48 0 35. 36. 7 − 2 ⋅ 3 + 32 7 − 2 ⋅ 3 + 9 7 − 6 + 9 10 = = = =2 5(2 − 1) 5(1) 5 5 6 2 + 4 ⋅ 4 + 23 2 37 − 5 Check: 456 × 8 3648 36 + 4 ⋅ 4 + 8 37 − 25 36 + 16 + 8 = 12 60 = 12 =5 = 37. x + 6 = 8 + 6 = 14 27. number of cards number of number of = ÷ for each person cards friends = 238 ÷ 19 12 R 10 19 238 −19 48 −38 10 Each friend will receive 12 cards. There will be 10 cards left over. 38. 5 + x = 5 + 9 = 14 39. a. |−9| = 9 because −9 is 9 units from 0. b. |8| = 8 because 8 is 8 units from 0. c. |0| = 0 because 0 is 0 units from 0. 40. a. |4| = 4 because 4 is 4 units from 0. b. |−7| = 7 because −7 is 7 units from 0. 41. −2 + 25 = 23 42. 8 + (−3) = 5 43. 2a − b = 2(8) − (−6) = 16 − (−6) = 16 + 6 = 22 Copyright © 2020 Pearson Education, Inc. 69 Chapter 2: Integers and Introduction to Solving Equations 44. x − y = −2 − (−7) = −2 + 7 = 5 45. −7 ⋅ 3 = −21 46. 5(−2) = −10 47. 0 ⋅ (−4) = 0 48. −6 ⋅ 9 = −54 70 ISM: Algebra Foundations 49. 3(4 − 7) + (−2) − 5 = 3(−3) + (−2) − 5 = −9 + (−2) − 5 = −11 − 5 = −16 50. 4 − 8(7 − 3) − (−1) = 4 − 8(4) − (−1) = 4 − 32 − (−1) = 4 − 32 + 1 = −28 + 1 = −27 Copyright © 2020 Pearson Education, Inc.