Chapter 2. Section < , 2, 0, 3. Objective A Exercises, pages , 3, 1, , 0, 5, 9 37.

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1 Chapter 2 Section 2.1 Objective A Exercises, pages is 3 units to the right of is 4 units to the left of is 6 units to the right of A B C D E F G H I A is 4, and C is A B C D E F G H I A is 7, and D is > > < > < < , 2, 0, , 3, 1, , 0, 5, , 7, 5, 4, , 7, 2, 5, 10 Objective B Exercises, pages n 47. d 49. the opposite of negative thirteen 51. the opposite of negative p 53. five plus negative ten 55. negative fourteen minus negative three 57. negative thirteen minus eight 59. m plus the opposite of n 61. ( 7) = ( 61) = (46) = ( 73) = ( z) = z 71. (p) = p Objective C Exercises, pages

2 Section x x y , > , < , < x = x x x , 4 6, 4, 7, , 9 9, 5 9, 7, 5, 4 4, 7 7, 9 9 5, 4 4 Objective D Exercises, pages Strategy To find the wind chill factor, use the given table. Find the number where the column with 10 and the row with 20 cross. Read the number 24. The wind chill factor is 24 F Strategy To find the cooling power, use the given table. Find the number where the column with 15 and the row with 10 cross. Read the number 40. The cooling power is 40 F Strategy To find the situation which feels colder: From the given table, find the wind chill factor with a temperature of 30 F with a 5-mph wind and the wind chill factor with a temperature of 20 F with a 10-mph wind. Compare the wind chill factors. The wind chill factor with a temperature of 30 F and 5- mph wind is 36 F. The wind chill factor with a temperature of 20 F and 10- mph wind is 46 F. 36 > F with a 10-mph wind feels colder. 3, 8 8, 5 5, ,2 2 10, 8, 2, 3, The absolute value of a number is the distance from zero to the number on the number line. If y 11, then y must be a number that is 11 units from 0 on the number line. Therefore, y is 11 or x must be less than 7 and greater than 7. 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6

3 24 Chapter 2: Integers 121. Strategy a. To find the earnings per share in 2000, read the number in the bar graph below the bar corresponding to b. To find the earnings per share in 2002, read the number in the bar graph below the bar corresponding to a. The earnings per share for 2000 were 27. b. The earnings per share for 2002 were Strategy To find a year in which Mycogen had a profit, use the bar graph to find a year in which earnings per share were positive. The only recorded positive earnings per share were 11. Earnings per share were 11 in Mycogen did earn a profit during the years shown. Mycogen earned a profit in Strategy To determine which stock showed the least net change, compare the absolute values of the numbers 1 and 2. The smaller number represents the least net change. 1 1, < 2 Stock B showed the least net change Strategy To determine which quarter has the greater loss, compare the absolute values of the numbers 26,800, and 24,900. The larger number corresponds to the quarter with the greater loss. 26,800 26,800 24,900 24,900 26,800 > 24,900 The loss was greater during the third quarter. Critical Thinking 2.1, page a. Two numbers that are 4 units from 2 on the number line are 2 and 6. b. Two numbers that are 5 units from 3 on the number line are 2 and a. Enter the number 9. Press the +/ key. b. Enter the number 20. Press the +/ key. c. Enter the number 148. Press the +/ key. d. Enter the number 573. Press the +/ key Since x is an integer and x 10, x must be less than 10 and greater than 10: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Of these values of x, the numbers for which x 6 are: 9, 8, 7, 7, 8, 9.

4 Section Section 2.2 Objective A Exercises, pages ( 8) = = = ( 10) = ( 5) = ( 5) = = ( 5) + ( 10) = = ( 15) + ( 6) = ( 14) = ( 54) = ( 12) + ( 15) = 15 + ( 15) = ( 3) + 29 = = ( 22) ( 5) = ( 5) = 7 + ( 5) = ( 18) = ( 18) = 10 + ( 18) = ( 31) = = = ( 21) = = ( 3) + ( 8) + 12 = = x + ( 7) ( 3) + ( 4) = 1 + ( 4) = a. 73,920,000,000 + ( 68,668,000,000) = 142,588,000,000 The total of the U.S. balance of trade in Japan and China is 142,588,000,000. b. 32,095,000,000 + ( 28,305,000,000) = 60,400,000,000 The total of the U.S. balance of trade with Canada and Germany is 60,400,000,000. c. 73,920,000,000 + ( 28,305,000,000) = 102,225,000,000 The total of the U.S. balance of trade with Japan and Germany is 102,225,000, a + b ( 8) + ( 3) = 8 + ( 3) = x + y ( 5) + ( 7) = 5 + ( 7) = a + b + c 10 + ( 6) + 5 = = = ( 18) = = 3 + z No, 8 is not a solution of the equation 6 = 3 + z. 55. x + ( y) + z ( 2) + ( 8) + ( 11) = 2 + ( 8) + ( 11) = 6 + ( 11) = The Addition Property of Zero 59. The Associative Property of Addition

5 26 Chapter 2: Integers m = = 15 Yes, 8 is a solution of the equation 7 + m = z = z No, 4 is not a solution of the equation 1 + z = z + 2. Objective B Exercises, pages = 6 + ( 9) = = 9 + ( 4) = ( 4) = = ( 4) = = = 10 + ( 7) = ( 7) ( 4) = = ( 16) = = ( 24) = = ( 41) 65 = 41 + ( 65) = ( 28) = = ( 4) = = = 9 + ( 6) = t r ( 33) = = 82 The difference between the highest and lowest temperatures ever recorded in South America is 82 C = 4 + ( 3) + ( 2) = 7 + ( 2) = ( 7) 8 = ( 8) = 19 + ( 8) = ( 8) = 4 + ( 12) + 8 = = = 16 + ( 47) + ( 63) + ( 12) = 63 + ( 63) + ( 12) = ( 12) = ( 6) + 8 = = = ( 14) + 7 = = = = 9 + ( 12) ( 5) = ( 5) = 3 + ( 5) = ( 3) 7 = ( 7) = ( 7) = 12 + ( 7) = ( 10) 4 = ( 4) = ( 4) = 6 + ( 4) = x y ( 3) 9 = 3 + ( 9) = x ( y) ( 3) ( 9) = = a b c 4 ( 2) 9 = ( 9) = 6 + ( 9) = x y ( z) 9 3 ( 30) = 9 + ( 3) + 30 = = 18

6 Section x 7 = = 10 Yes, 3 is a solution of the equation x 7 = w = No, 2 is not a solution of the equation 5 w = t 5 = 7 + t = 1 Yes, 6 is a solution of the equation t 5 = 7 + t. Objective C Exercises, pages Strategy a. To find the difference, subtract the elevation of Death Valley ( 86) from the elevation of Mt. Aconcagua (6,960). b. To find the difference, subtract the elevation of the Qattara Depression ( 133) from the elevation of Mt. Kilimangaro (5,895). a. 6,960 ( 86) = 6, = 7,046 The difference in elevation is 7,046 m. b. 5,895 ( 133) = 5, = 6,028 The difference in elevation is 6,028 m Strategy To determine for which continent the difference between the highest and lowest elevations is smallest: Find the difference between the highest and lowest elevation for each continent. Compare the differences. Africa: 5,895 ( 113) = 5, = 6,028 Asia: 8,848 ( 400) = 8, = 9,248 Europe: 5,643 ( 28) = 5, = 5,671 America: 6,960 ( 86) = 6, = 7,046 5,671 < 6,028 < 7,046 < 9,248 The difference between the highest and lowest elevations is smallest in Europe.

7 28 Chapter 2: Integers 137. Strategy To find the difference, subtract the average temperature at 40,000 ft ( 70) from the average temperature at 12,000 ft (16). 16 ( 70) = = 86 The difference in temperature is Strategy To find how much colder, subtract the average temperature at 30,000 ft ( 48) from the average temperature at 20,000 ft ( 12). 12 ( 48) = = 36 The temperature is 36 colder Strategy To find the golfer s score, substitute 49 for N and 52 for P in the given formula and solve for S. S = N P S = S = 49 + ( 52) S = 3 The golfer s score is Strategy To find d, replace a by 7 and b by 12 in the given formula and solve for d. Critical Thinking 2.2, page 116 d a b d 7 12 d 7 12 d 19 d = 19 The distance between the two points is 19 units a. The opposite, or additive inverse, of 5 is 5. The difference between 5 and 5 is 5 ( 5) = = 10, which is not 0. The additive inverse of 0 is 0. The difference between 0 and 0 is 0 0 = 0. The statement is sometimes true. Section 2.3 b. When adding two numbers with the same sign, we add the absolute values of the numbers and then attach the sign of the addends. When adding two negative numbers, the signs of the addends are negative. Therefore, we would attach a negative sign on the sum. The statement is always true. Objective A Exercises, pages = ( 3) = 6 7. (9)(2) = ( 4) = (2) = ( 5)( 5) = ( 7)(0) = (3) = 42

8 Section (4) = ( 8)( 26) = ( 27) = (23) = ( 34) = ( 8) 3 = 32 3 = ( 6)(5)(7) = 30(7) = ( 7)( 4) = 56( 4) = ( 20) = ( 6) = q(r) = qr 41. a. 4,144,000(4) = 16,576,000 The annual net income for Barnes & Noble would be 16,576,000. b. 23,480,000(4) = 93,920,000 The annual net income for Bradlees would be 16,576,000. c. 118,000,000(4) = 472,000,000 The annual net income for J.C. Penney would be 472,000, The Multiplication Property of One 45. The Associative Property of Multiplication (5 10) = ( 6 5) ( 14) = xy ( 3)( 8) = 3( 8) = xyz ( 6)(2)( 5) = 6(2)( 5) = 12( 5) = n 7( 51) = ab 8(7)( 1) = 56( 1) = st 5( 40)( 8) = 200( 8) = 1, x = No, 3 is not a solution of the equation 5x = = 8a No, 0 is not a solution of the equation 8 = 8a = 3c = 27 Yes, 9 is a solution of the equation 27 = 3c. Objective B Exercises, pages ( 3) = ( 64) ( 8) = = ( 5) = ( 7) = ( 162) ( 162) = ( 5) = ( 92) ( 4) = x

9 30 Chapter 2: Integers ,085,000 3 = 9,695,000 The average monthly net income for Ames was 9,695, a b ( 36) ( 4) = 36 ( 4) = ( a) ( b) ( 36) ( ( 4)) = 36 4 = x y 42 7 = x y = c = 6 Yes, 18 is a solution of the equation n No, 3 is not a solution of the equation. m 4 16 m = 2 Yes, 8 is a solution of the equation. Objective C Exercises, pages Strategy To find the average score, divide the combined scores ( 12) by the number of golfers (4) = 3 The average golf score was Strategy To find the average record low temperature for the first three months of the year: Add the average temperatures for January ( 70), February ( 66), and March ( 50). Divide the sum by the number of months (3) ( 66) + ( 50) = ( 50) = = 62 The average record low temperature for the first three months of the year is 62 F Strategy To find the average daily low temperature for the week: Add the seven temperature readings. Divide by ( 5) ( 1) + ( 12) + ( 14) + ( 8) = = 4 The average daily low temperature for the week was Strategy To find the wind chill factor, multiply the wind chill factor at 25 F with a 35 mph wind ( 12) by = 60 The wind chill factor is 60 F.

10 Section Strategy To find the next three numbers in the sequence: Find the multiplier by dividing the second number in the sequence ( 4) by the first number (2). Use the multiplier to find the successive numbers in the sequence ( 2) = ( 2) = ( 2) = 64 The next three numbers in the sequence are 16, 32, and Strategy To find the next three numbers in the sequence: Find the multiplier by dividing the second number in the sequence ( 5) by the first number ( 1). Use the multiplier to find the successive numbers in the sequence = = = 3,125 The next three numbers in the sequence are 125, 625, and 3,125. Critical Thinking 2.3, page a. We are looking for the largest possible product of two negative integers whose sum is 18. Find pairs of negative integers whose sum is 18 and look for a pattern ( 1) = 18; ( 17)( 1) = ( 2) = 18; ( 16)( 2) = ( 3) = 18; ( 15)( 3) = 45 The numbers are increasing. : 10 + ( 8) = 18; ( 10)( 8) = ( 9) = 18; ( 9)( 9) = ( 10) = 18; ( 8) ( 10) = ( 11) = 18; ( 7)( 11) = 77 The numbers are decreasing. The largest possible product of two negative integers whose sum is 18 is 81. b. We are looking for the smallest possible sum of two negative integers whose product is 16. List all the possible pairs of negative integers whose product is ( 1) = 16; 16 + ( 1) = 17 8( 2) = 16; 8 + ( 2) = 10 4( 4) = 16; 4 + ( 4) = 8 Of the numbers 17, 10, and 8, 17 is the smallest number. The smallest possible sum of two negative integers whose product is 16 is By substituting negative integers for x in the inequality 1 3x < 12, it can be shown that 3, 2, and 1 are the only negative integers that satisfy the inequality. Section 2.4 Objective A Exercises, page x 6 = 9 x = x = 15 The solution is 15.

11 32 Chapter 2: Integers 3. 8 = y = y = y The solution is x 5 = 12 x = x = 7 The solution is = z = z = z The solution is x + 12 = 4 x = 4 12 x = 8 The solution is = c = c = c The solution is x = x 6 = 4 6 x = 2 The solution is = n = n = n The solution is m = 15 3m m = 5 The solution is = 5v v 5 2 = v The solution is x = 40 8 x x = 5 The solution is x = 100 5x x = 20 The solution is x = 0 4 x x = 0 The solution is r = 16 2r r = 8 The solution is = 18w 72 18w = w The solution is 4. Objective B Exercise, page The unknown number: n ten less than a number is fifteen n 10 = 15 n = n = 25 The number is The unknown number: n zero is equal to fifteen more than some number 0 = n = n = n The number is = 6v v 6 10 = v The solution is 10.

12 Section The unknown number: n sixteen equals negative two times a number 16 = 2n n 2 8 = n The number is The unknown number: n zero is equal to the product of negative six and a number 0 = 6n 0 6 6n 6 0 = n The number is Strategy To find the U.S. balance of trade in 1998, write and solve an equation using x to represent the U.S. balance of trade in the balance of trade in 1950 was $230,843 million more than the balance of trade in ,043 = x + 230,843 1, ,843 = x + 230, , ,800 = x The U.S. balance of trade in 1998 was $229,800 million. 43. Strategy To find this morning s temperature, write and solve an equation using x to represent this morning s temperature. the temperature now is 5 higher than it was in this morning 8 = x = x = x The temperature this morning was 3 C. 45. Strategy To find the selling price of the car, replace P by 925 and C by 12,600 in the given formula and solve for S. P = S C 925 = S 12, ,600 = S 12, ,600 13,525 = S The selling price of the car should be $13, Strategy To find the assets, replace N by 11 and L by 4 in the given formula and solve for A. N = A L 11 = A = A = A The assets are $15 million.

13 34 Chapter 2: Integers Critical Thinking 2.4, page a. False. For example, the solution of the equation 5x = 0 is 0. Section 2.5 b. False. For example, the solution of the equation 5x = 5 is 1, a negative number. c. False. For example, the solution of the equation 5x = 5 is 1, a positive number. Objective A Exercises, pages = 3 6 = 3 + ( 6) = (3 5) 2 = 2( 2) 2 = 4 2 = 4 + ( 2) = = 4 + ( 9) = (2 4) 4 = 4 ( 2) 4 = 8 4 = 8 + ( 4) = = 4 + ( 4) + ( 3) = 0 + ( 3) = = 27 8 = 27 + ( 8) = (6 2) 6 = = 12 6 = = 8 + ( 9) + 2 = = (1 5) = 6 2( 4) = 6 ( 8) = = = 6 ( 36) = = = = 8 21 = 8 + ( 21) = = = 4 + ( 15) + ( 1) = 11 + ( 1) = = = = = ( 17) = 49 + ( 17) = = 12 ( 2) (2) = (2) = (2) = = ( 12) = 42 + ( 12) = = = = 27 + ( 9) + ( 2) + ( 7) + 18 = 36 + ( 2) + ( 7) + 18 = 38 + ( 7) + 18 = = = ( 18) ( 9) = ( 18) ( 9) = 16 + ( 32) = = = = 27

14 Section a + 2b 3( 2) + 2(4) = 6 + 2(4) = = (ac) 16 (( 2)( 1)) = 16 2 = bc (2a) 4( 1) ((2)( 2)) = 4( 1) ( 4) = ( 4) ( 4) = b 2 c = 16 + ( 1) = b a 2 4c = ( 1) = 36 + ( 4) = d b c = 1 b d c a = d a = 25 5 =

15 36 Chapter 2: Integers 49. d a 2 3c = 25 3( 1) = 25 ( 3) = = 28 Critical Thinking 2.5, page = ( 6) = ( 6) = 4 + ( 9) = = = 5 We are looking for the smallest integer greater than 5. The smallest integer greater than 5 is The smallest integer greater than a. x 2 2 x No, 4 is not a solution of the equation. b. x 3 3x 2 5x = 0 Yes, 3 is not a solution of the equation. Chapter Review Exercises, pages eight minus negative one ( 40)( 5) = a b ( 27) ( 3) = 27 ( 3) = 9 is 4.

16 Chapter Review = ( 13) = = 6y 24 6y = y The solution is ( 3) = ( 7) 15 ( 12) = ( 15) + 12 = 1 + ( 15) + 12 = = ab ( 2)( 9) = 2( 9) = ( 13) + ( 6) = 5 + ( 6) = (4) = = = = = 4 + ( 2) + ( 6) = 2 + ( 6) = x y ( 1) 3 = 1 3 = 1 + ( 3) = ( 3) = = 8 The difference between the number of strokes made by Pitcock and the number by King is 8 strokes The Commutative Property of Multiplication t = = 3 Yes, 9 is a solution of the equation 6 t = ( 7) = = = (2)( 6)( 1) = 10( 6)( 1) = 60( 1) = ( 9) ( 10) = ( 10) = 2 + ( 10) = a b 2a = 1 2( 2) = 1 ( 4) = = > = The unknown number: n forty-eight is the product of negative six and some number 48 = 6n n 6 8 = n The number is ( 28) = = 13

17 38 Chapter 2: Integers 30. Strategy To find the colder temperature, compare the numbers 4 and 12. The smaller number represents the colder temperature. 4 > 12 The colder temperature is 12 C. 31. Strategy To find the boiling point of neon: Find the highest boiling point shown in the table. Multiply the highest boiling point by 7. The highest boiling point shown in the table is (7) = 245 The boiling point of neon is 245 C. 32. Strategy To find the temperature, add the increase (5) to the previous temperature ( 8) = 3 The temperature is 3 C. 33. Strategy To find d, replace a by 7 and b by 5 in the given formula and solve for d. Chapter Test, pages d a b d 7 5 d 7 5 d 12 d = 12 The distance between the two points is 12 units. 1. negative three plus negative five The Commutative Property of Addition = = = > ( 3) 12 = = = a b c = 6 ( 2) 11 = = 8 11 = ( 49) = ( 5) = , (3), 9, ( 11) x = 8 17 ( 9) No, 9 is not a solution of the equation 17 x = is 2 units to the right of Strategy To find the difference in scores, Woods' score ( 19) from Nicklaus' score (5). 5 ( 19) = = 24 The difference in scores was 24 strokes ( 15) = = a + b ( 11) + ( 9) = ( x)( y) ( ( 4)) ( ( 6)) = 4 6 = 24

18 Cumulative Review bc (c a) 3 (2 4 ( 1)) ( 1 + ( 2)) 3 = 8 ( 3) 3 = 8 ( 27) = = c 11 = 5 c = c = 16 The solution is = ( 4) = ( 2) = 4 ( 6) = = x y ( 56) = xy 3 ( 2) ( 10) = 3 20 = w = w w = 11 The solution is = Strategy To find the temperature, add the increase (11) to the previous temperature ( 6) = 5 The temperature is 5 C. 30. The unknown number: n the wind chill at 30 F with a 40 mph wind is Four times the wind chill factor at 30 F with a 40 mph wind n = 4 ( 25) n = 100 The wind chill factor is 100 F. 31. Strategy To find the temperature from yesterday, add the increase (8) to today's temperature ( 13) = 5 The temperature is 5 C. 32. d a b d 4 ( 12) = 16 The solution is Strategy To find the assets, substitute 18 for N and 6 for L in the given formula and solve for A. N = A L 18 = A = A = A The assets are worth $24 million. Cumulative Review Exercises, pages ( 32) = = = 12,000 3, , = = = = 18 + ( 16) = , xy = = 2, ( 14) = 21

19 40 Chapter 2: Integers ( 17) = = ( 32) = 8 + ( 32) = = = = = 4 The factors of 44 are 1, 2, 4, 11, 22, and x 4 y = = 1, Given place value , ,874 rounded to the nearest thousand is 630, , a b ( 4) ( 5) = = = 2, = x = 48 3x x = 16 The solution is = 16 ( 2) + 8( 3) = 8 + 8( 3) = 8 + ( 24) = c d ( 32) ( 8) = 32 ( 8) = a b < ( 7) = p = p = 3 12 p = 9 The solution is a a b = 4(5) + 27 = = , ,609 10, = 21 + ( 5) = ,352 1,986 7,000 2,000 5, = = 2,

20 Cumulative Review Strategy To find the land area, add the land area prior to the purchase (891,364) to the amount of land purchased (831,321). 891, ,321 1,722,685 The land area of the United States after the Louisiana purchase was 2 1,722,685 mi. 32. Strategy To find the age, subtract the year of the birth (1879) from the year of his death (1955) Albert Einstein was 76 years old when he died. 33. Strategy To find the amount, subtract the down payment (3,550) from the cost (17,750). 17, 750 3,550 14,200 The amount to be paid is $14, Strategy To find the trade balance for services, subtract the balance for goods ( 35,393 million) from the total trade balance ( 28,714 million). 28,714 ( 35,393) = 28, ,393 = 6,779 The trade balance for services is $6,779,000, Strategy To find the amount: Add the sales figures for the first three quarters (28, , ,700). Subtract the sum from the goal for the year (120,000). 28,550 34,850 31,700 95, , ,100 24,900 You must sell $24,900 in the last quarter to meet the goal. 38. Strategy To find the score, substitute 198 for N and 206 for P in the given formula and solve for S. 34. Strategy To find the cost of the land, multiply the number of acres (25) times the cost per acre (3,690). 3, ,250 The cost of the land is $92, Strategy To find the temperature, add the increase (7) to the original temperature ( 12) = 5 The temperature is 5 C. S = N P S = S = 8 The golfer s score is 8.