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1 CHAPTER TWO, FORM A 37 CHAPTER TWO, FORM A ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation ( 3c) = 4( c 5) + 3c + 7 ( ) c y y = x 3 x 19 + = Decide whether the equation ( 4 x ) + 3 = 8( 5 x) 3 10 is conditional, an identity, or a contradiction. Give its solution set Solve for c: 4bc + 5 c = 5. b 3 6. Solve for f: 4f 5= 7h+ fg 6. For Exercises 7-1, solve the problem. 7. At the very first Indianapolis 500-mile race in 1911, Ray Harroun won in a time of 6.7 hours. What was his average speed in miles per hour, rounded to the nearest tenth? 8. Dick Sauerman invested $3900 in a mutual fund one year ago. During the year, his fund increased in value by $ What interest rate has Dick s investment earned? 9. The sale price on a new pair of Aviator sunglasses is $55. This represents 15% off the regular price. What is the regular price?

2 38 CHAPTER TWO, FORM A 10. Two trains leave at the same time from cities that are 450 miles apart, traveling toward each other on adjacent tracks. One train is traveling 0 miles per hour slower than the other. They pass each other after 3 hours. Find the speed of each train Gail Brown invested some money at 9% and $100 more than that at 6%. Her total annual interest was $96. How much did she invest at each rate? Find the measure of each angle. ( 3x + 30) x x 1. For Exercises 13-15, solve the inequality. Give the solution set in both interval and graph forms. ( ) d d x y Luke has test grades of 85, 87, and 77 on his first three algebra tests. If he wants an average of at least 84 after his fourth test, what are the possible scores he can make on his fourth test? 16.

3 CHAPTER TWO, FORM A A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 40x+ 3000, while the revenue is R = 60x. For what values of x is R at least equal to C? 17. For Exercises 18-19, let = { 1, 4, 7, 8} and B = {, 4, 9,13} A. 18. Find A B Find A B 19. For Exercises 0-3, solve the compound or absolute value inequality. Give the solution set in both interval and graph forms. 0. 4x + 3 > 11 or 3x t y < 6 or 3y 1< x > 3. For Exercises 4-5, solve the absolute value equation. 4. 3x + 4 = x t = 15 5.

4 40 CHAPTER TWO, FORM B CHAPTER TWO, FORM B ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation. ( ) ( ) z 4 3z = 6 3z 1. ( ). 0.8 y 9 = y. 3. x 7 x 43 + = Decide whether the equation ( x + 6) = 3( 8 x) ( x 17) 7 4 is conditional, an identity, or a contradiction. Give its solution set Solve for t: t + 7 r = 5. t 6. Solve for g: 4g 5= 7h+ fg 6. For Exercises 7-1, solve the problem. 7. A.J. Foyt won his first of four Indianapolis 500-mile races in 1961, in a time of 3.59 hours. What was his average speed in miles per hour, rounded to the nearest tenth? 8. The sale price on a new lawn mower is $3. This represents 0% off the regular price. What is the regular price? 9. Joe Borowski invested $5700 in a mutual fund one year ago. During the year, his fund increased in value by $ What interest rate has Joe s investment earned?

5 CHAPTER TWO, FORM B Two distance runners leave from the same point at the same time, traveling in opposite directions. One runs miles per hour faster than the other. After hours, they are 36 miles apart. Find the speed of each runner Sherry Akey invested some money at 8% and $100 more than that at 6%. Her total annual interest was $48. How much did she invest at each rate? Find the measure of each angle. ( 3x + 30) x ( x + 50) 1. For Exercises 13-15, solve the inequality. Give the solution set in both interval and graph forms. ( ) t t x x Sam has test grades of 75, 77, and 69 on his first three algebra tests. If he wants an average of at least 80 after his fourth test, what are the possible scores he can make on his fourth test? 16.

6 4 CHAPTER TWO, FORM B 17. A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 0x+ 3600, while the revenue is R = 60x. For what values of x is R at least equal to C? For Exercises 18-19, let = { 8, 9,11,13} and B = { 10,1,13,15} A Find A B Find A B. 19. For Exercises 0-3, solve the compound or absolute value inequality. Give the solution set in both interval and graph forms. 0. 4x 3 < 11or 3x > x 1< 3 and 3x t r + 3 < 15. For Exercises 4-5, solve the absolute value equation. 4. x + 7 = 6x t = 17 5.

7 CHAPTER TWO, FORM C 43 CHAPTER TWO, FORM C ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation. ( ) ( ) z 4 + 3z = z ( ) y+ 9 = 0.4y. 3. z + 5 3z z = Decide whether the equation ( x + 6) = 5( x + 1) + 3( 4 x) + ( 1x 17) 4 + is conditional, an identity, or a contradiction. Give its solution set Solve for y: 4+ y = 5 y z Solve for k: k 3= 6h fk 6. For Exercises 7-1, solve the problem. 7. Mario Andretti won his only Indianapolis 500-mile race in 1969, in a time of 3.19 hours. What was his average speed in miles per hour, rounded to the nearest tenth? 8. The sale price on a new motorcycle is $715. This represents 5% off the regular price. What is the regular price? 9. Mark Guthrie invested $7400 in a mutual fund one year ago. During the year, his fund increased in value by $703. What interest rate has Mark s investment earned?

8 44 CHAPTER TWO, FORM C 10. Two airplanes leave Chicago s Midway airport at the same time, traveling in opposite directions. One travels 5 miles per hour faster than the other. After hours, they are 490 miles apart. Find the speed of each airplane Bobbi Reutter invested some money at 7% and $100 less than that at 8%. Her total annual interest was $58. How much did she invest at each rate? Find the measure of each angle. ( 3x 10) x ( 4x 50) 1. For Exercises 13-15, solve the inequality. Give the solution set in both interval and graph forms ( t ) ( 6t + 1) x x < Alissa has test grades of 90, 87, and 79 on her first three algebra tests. If she wants an average of at least 80 after her fourth test, what are the possible scores she can make on the fourth test? 16.

9 CHAPTER TWO, FORM C A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 35x+ 3000, while the revenue is R = 75x. For what values of x is R at least equal to C? For Exercises 18-19, let = { 5, 6, 7, 8} and B = { 6, 8,10,1} A Find A B Find A B 19. For Exercises 0-3, solve the compound or absolute value inequality. Give the solution set in both interval and graph forms. 0. 3x + 5 < 8 or x x + 4 < 19 and x < t x + 5 > For Exercises 4-5, solve the absolute value equation. 4. x 5 = 9x t = 18 5.

10 54 CHAPTER TWO, FORM F CHAPTER TWO, FORM F ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation ( 3 r ) + 7 = 5( r ) ( g ) g = z + 8 z = z Decide whether the equation ( x 4) + 3( 5 x) 9 = 9( x ) 6 is conditional, an identity, or a contradiction. Conditional Identity Contradiction Solve for b: ab 5 = b 3 b +15 b = 3a 15 b = 3 a 1 b = 3ab 15 b = 15 3a + b 5.

11 CHAPTER TWO, FORM F Solve for k: k 3= 6h fk 6h 3 k = f + + f k = 3 6h 6h fk+ 3 k = 3 6h k = 6. + f For Exercises 7-1, solve the problem. 7. Arie Luyendyk won the Indianapolis 500-mile race in 1990, in a record time of.69 hours. What was his average speed in miles per hour, rounded to the nearest tenth? mph mph mph mph The sale price on a diamond ring is $136. This represents 11% off the regular price. What is the regular price? $34.96 $ $ $ Bruce Sutter invested $8300 in a mutual fund one year ago. During the year, his fund increased in value by $ What interest rate has Bruce s investment earned? 7.% 7.8% 1.8% 13.8% Two cars leave at the same time from towns that are 180 miles apart, traveling toward each other. One car travels 10 miles per hour faster than the other. They meet each other after two hours. Find the speed of the faster car. 40 mph 50 mph 60 mph 75 mph Lynn Ogen invested some money at 9% and $100 less than that at 7%. Her total annual interest was $73. How much did she invest at 7%? $ $ $50.00 $

12 56 CHAPTER TWO, FORM F 1. Find the measure of each angle. ( 3x 10) x ( 4x 50) 30,70,80 5,65,90 30,50, ,50,90 For Exercises 13-14, solve the inequality. Give the solution set in interval form x > 6 (,9) (, ( 9, ) 4) (, ) ( t 3) 8t (, 3] 5 3 [ 3, ), (,15] For Exercise 15, solve the inequality. Give the solution set in graph form. 15. x

13 CHAPTER TWO, FORM F Luke has test grades of 85, 87, and 97 on his first three algebra tests. If he wants an average of at least 88 after his fourth test, what are the possible scores he can make on his fourth test? x > 83 x 83 x > 73 x A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 30x+ 6000, while the revenue is R = 60x. For what values of x is R at least equal to C? x 00 x 400 x 000 x A. For Exercises 18-19, Let = { 7, 9,11,13} and B = { 6,11,1,13} 18. Find A B. {, 7, 9,1} 11,13 { 6, 7, 9,11,1,13} { } 19. Find A B. {, 7, 9,1} 11,13 { 6, 7, 9,11,1,13} { } For Exercises 0-1, solve the compound or absolute value inequality. Give the solution set in interval form. 0. 8x 1 < 15 or 3x 5 > 7 [,4] (, 4 (, ] [ 4, ) ) ( ) ( 4, ), t 9 1 7] (, 1] [ 7, ) ) ( 1) ( 7, ) [ 1, ( 1, 7, 1.

14 58 CHAPTER TWO, FORM F For Exercises -3, solve the compound or absolute value inequality. Give the solution set in graph form. ( ) 6. 3x or 3 x 1. No solution 3. 5 r + 7 > 3 3. For Exercises 4-5, solve the absolute value equation. 4. x 5 = 7x , , t = , 5 33, 5.

15 46 CHAPTER TWO, FORM D CHAPTER TWO, FORM D ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation ( 3 ) + 7 = 5( r ) 9 ( ) r g g = z + 8 z = z Decide whether the equation ( x 4) + 3( 5 x) 9 = 9( x ) 6 is conditional, an identity, or a contradiction. Give its solution set Solve for b: ab 5 = b Solve for f: f 3= 9h fg 6. For Exercises 7-1, solve the problem. 7. Arie Luyendyk won the Indianapolis 500-mile race in 1990, in a record time of.69 hours. What was his average speed in miles per hour, rounded to the nearest tenth? 8. The sale price on a diamond ring is $136. This represents 11% off the regular price. What is the regular price? 9. Bruce Sutter invested $8300 in a mutual fund one year ago. During the year, his fund increased in value by $ What interest rate has Bruce s investment earned?

16 CHAPTER TWO, FORM D Two cars leave at the same time from towns that are 180 miles apart, traveling toward each other. One car travels 10 miles per hour faster than the other. They meet each other after two hours. Find the speed of each car Rhonda Andjelich invested some money at 9% and $100 less than that at 7%. Her total annual interest was $81. How much did she invest at each rate? Find the measure of each angle. ( 3x 50) ( x 10) ( x +10) 1. For Exercises 13-15, solve the inequality. Give the solution set in both interval and graph forms. ( ) t t x x > Lauren has test grades of 75, 87, and 77 on her first three algebra tests. If she wants an average of at least 84 after her fourth test, what are the possible scores she can make on the fourth test? 16.

17 48 CHAPTER TWO, FORM D 17. A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 50x+ 6000, while the revenue is R = 80x. For what values of x is R at least equal to C? For Exercises 18-19, let = { 7, 9,11,13} and B = { 6,11,1,13} A Find A B Find A B 19. For Exercises 0-3, solve the compound or absolute value inequality. Give the solution set in both interval and graph forms x 1< 15 or 3x 5 > 7 0. ( ) x or 3 x t r + 7 > 3 3. For Exercises 4-5, solve the absolute value equation. 4. x 5 = 7x t = 19 5.

18 CHAPTER TWO, FORM E 49 CHAPTER TWO, FORM E ALGEBRA FOR COLLEGE STUDENTS NAME SECTION For Exercises 1-3, solve the equation z ( 4 + 3z) = ( z 1) ( ) y+ 9 = 0.4y z + 5 3z z = Decide whether the equation ( x + 6) = 5( x + 1) + 3( 4 x) + ( 1x 17) 4 + is conditional, an identity, or a contradiction. Conditional Identity Contradiction Solve for y: 4+ y = 5 y z 4z y = 5z 5 y = 5 z 5z 4+ y y = y = z 5. y + 4 5

19 50 CHAPTER TWO, FORM E 6. Solve for f: 4f 5= 7h+ fg 7h + 5 f = f = 7h+ g+ 1 4 g 7h+ fg+ 5 4 g f = f = 4 7h + 5 For Exercises 7-1, solve the problem. 7. Mario Andretti won his only Indianapolis 500-mile race in 1969, in a time of 3.19 hours. What was his average speed in miles per hour, rounded to the nearest tenth? mph 13.4 mph 15.6 mph mph The sale price on a new motorcycle is $715. This represents 5% off the regular price. What is the regular price? $ $ $ $ Lee Smith invested $7400 in a mutual fund one year ago. During the year, his fund increased in value by $703. What interest rate has Lee s investment earned? 8.7% 9.5% 10.5% 11.5% Two airplanes leave Chicago s Midway airport at the same time, traveling in opposite directions. One travels 5 miles per hour faster than the other. After hours, they are 490 miles apart. Find the speed of the faster airplane. 110 mph 135 mph 160 mph 185 mph Bobbi Reutter invested some money at 7% and $100 less than that at 8%. Her total annual interest was $58. How much did she invest at 7%? $ $ $ $

20 CHAPTER TWO, FORM E Find the measure of each angle. ( 3x + 30) x x 40,40,100 45,45,90 5,5, ,30,10 For Exercises 13-14, solve the inequality. Give the solution set in interval form x < 1 3 ( 16, ) (,16),,9 13. ( 9 ) ( ) ( ) ( 6t + 1 t ) 14 3 (,, (, 4] 0] [, ) For Exercise 15, solve the inequality. Give the solution set in graph form x

21 5 CHAPTER TWO, FORM E 16. Luke has test grades of 85, 87, and 77 on his first three algebra tests. If he wants an average of at least 84 after his fourth test, what are the possible scores he can make on his fourth test? x > 87 x 87 x > 77 x A product will break even or produce a profit only if the revenue R (in dollars) from selling the product is at least the cost C (in dollars) of producing it. Suppose that the cost to produce x units of wallpaper is C = 40x+ 3000, while the revenue is R = 60x. For what values of x is R at least equal to C? x 30 x 150 x 000 x For Exercises 18-19, Let = { 5, 6, 7, 8} and B = { 6, 8,10,1} 18. Find A B. A. {, 7,10,1} 6, 8 { 5, 6, 7, 8,10,1} { } 19. Find A B. {, 7,10,1} 6, 8 { 5, 6, 7, 8,10,1} { } For Exercises 0-1, solve the compound or absolute value inequality. Give the solution set in interval form. 0. 3x + 5 < 8 or x ) (, 1] ( 3, ) (, ) [ ) (, 3] [, 1 3, 1. 4t , 5 (, 5] 1, [ 5, 5] 1.

22 CHAPTER TWO, FORM E 53 For Exercises -3, solve the compound or absolute value inequality. Give the solution set in graph form.. 3 x + 4 < 19 and x < x + 5 > For Exercises 4-5, solve the absolute value equation. 4. x 5 = 9x , , , t = , ,

23 10 Answers to Diagnostic Pretest Answers to Diagnostic Pretest, Form A ,, 16,8, a 8. 0 y x = y = z > a b + 1a b y + 3y y 14. 1y + y 6 3b + 8a 7 1ab 7 4. y =, 3 5. x = 4, 3 6. ( 4, ) 7. AD + 4C B = z, 11z length = 5 meters a 30ab + 5b x x 4 x 5 5a + 7b ( 5a 7b 17. ( ) ) 18. ( v 9 )( v + 7) 19. ( 4y + 1 )( y 4) a b 8 1. m. 3y x 5 ( c + d ) ( c d ) 34.

24 Answers to Diagnostic Pretest 11 Answers to Diagnostic Pretest, Form B 1. D 30. B. D 3. A 4. D 5. B 6. D 7. B 8. C 9. C 10. B 11. D 1. C 13. D 14. C 15. D 16. A 17. B 18. C 19. D 0. A 1. B. B 3. C 4. B 5. B 6. A 7. D 8. A 9. C 31. D 3. D 33. A 34. A 35. A

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