CHAPTER 3 Linear Equations and Problem Solving

Transcription

1 CHAPTER Linear Equations and Problem Solving Section. Solving Linear Equations. x 9. x 6 5. Subtraction 7. Multiplication 9. Subtraction. Addition. 5 0 Original equation Subtract 5 from each side. 5 Combine like terms Divide each side b 5. x Simplif x 7. 9g 8 0 9g g 8 9g g 9. x 0 x 0 x x x 6. x 5 0 x x 5 x 5 x 6. 8z 0 8z 0 8z 8z 8 8 z x 9 0 x x 9 x 9 x x. p 0 p 0 p p p. 8 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

2 Section. Solving Linear Equations 9 5. x 7. 5t 6 t 5t t 6 t t 6t 6 6t 6 6t 6t 6 6 t 9. t 5 t t t 5 t t 5 0 False This equation has no solution.. x x x x x x x x x. x 6 x 6 x x 6 x x Identit This equation has infinitel man solutions. 5. x x x x x 5 7. x 5 x 5 x 5 x x x 5 6x 5 5 6x 5 6x 7 6x x 9 9. x x x x x x x 0 5. Verbal Model: Perimeter Length of a side Labels: Perimeter 5 (cm) Length of a side x (cm) Equation: 5 x 5 x 75 x The length of each side is 75 centimeters. 5. Verbal Model: Length Width Perimeter Labels: Width w inches Length w inches Perimeter 0 inches Equation: w w 0 w w 0 6w 0 w 0 and w 0 The width of the flag is 0 inches and the length is 0 inches. 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

3 0 Chapter Linear Equations and Problem Solving 55. Verbal Model: Revenue from Revenue from Total revenue main floor seats balcon seats Labels: Total revenue 500 Price per main floor seat 0 Number of main floor seats 00 Price per balcon seat 8 dollars dollars per seat seats dollars per seat Number of balcon seats x seats Equation: x x x 00 8x 00 8x x There were 50 balcon seats sold. 57. Yes. Subtract the cost of parts from the total to find the cost of labor. Then divide the labor cost b to find the number of hours spent on labor. Verbal Model: Cost of parts Hourl cost of labor Hours of labor Total cost Labels: Cost of parts 85 Hourl cost of labor dollars dollars per hour Hours of labor t hours Total cost 8 dollars Equation: 85 t t 8 85 t 99 t 99 t 9 The time spent on labor was 9 hours or hours. This answer could also be expressed as.5 hours or as hours and 5 minutes. 59. Verbal Model: Income for ear Amount of each Bonus pacheck Labels: Income for ear 7,0 dollars Amount of each pacheck x dollars per pacheck Bonus 800 dollars Equation: 7,0 x 800,0 x,0 x 0 x Each pacheck will be $0. 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

4 Section. Solving Linear Equations 6. Verbal Model: Total Pa per Number Pa for pa week of weeks training Labels: Total pa 65 Pa per week 0 Number of weeks x Pa for training 75 Equation: 65 0x x 560 0x x You internshipped for 8 weeks. dollars dollars per week weeks dollars 6. Substitute the solution into the original equation and simplif each side. x You are tring to isolate the variable term on the lefthand side of the equation. To do this, ou must eliminate the b subtracting : add x 5 x x 0 x 0 Note: x x x x 7. 5 x x 5 x x x 7. x x 75. 5t t 8t 8t 8t Identit The equation has infinitel man solutions x x 6 x x x x 6 The equation has no solution. 79. Verbal Model: Perimeter Length Width Labels: Perimeter 60 Width w Length w 0 meters meters meters Equation: 60 w 0 w 60 w w w w 00 w 50 w The length is 80 meters and the width is 50 meters. 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

5 Chapter Linear Equations and Problem Solving 8. Verbal Model: Total pa per hour Pa per hour 0.60 Number of units Labels: Total pa per hour 5.50 total dollars per hour Pa per hour 8.0 dollars per hour Number of units x units Equation: x x x x You must produce units per hour to earn $5.50 per hour. 8. Verbal Model: Total wages Rate for job Time at job Rate for job Time at job Labels: Total wages 00 dollars Rate for job 8.75 dollars per hour Time at job 0 hours Rate for job dollars per hour Time at job x hours Equation: x x 7.50 x 7.50 x.5 x You must work.5 hours, or hours and 0 minutes, at the second job. 85. Verbal Model: Weight of red box Weight of blue box 9 Weight of blue box Labels: Weight of red box R ounces Weight of blue box ounce Equation: R 9 R 9 R 9 R 6 The red box weighs 6 ounces. If ou remove three blue boxes from each side, the scale would still balance. The red box would balance the remaining six blue boxes, showing that the red box weighs 6 ounces. This illustrates the addition (or subtraction) propert of equalit. 87. False. Multipling each side of an equation b 0 ields 0 0. For example, multipling each side of the equation x 9 b 0, ields the equation 0 0. The equation x 9 has one solution, x ; however, the equation 0 0 is an identit and has infinitel man solutions. Because the original equation x 9 and the resulting equation 0 0 have different solutions, the are not equivalent equations. 89. False. An odd integer could be expressed as m and an even integer could be expressed as n. When the are added together, m n m nor m n. This expression could be written as m n ; it represents an odd number because it is not a multiple of. 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.

6 Section. Equations That Reduce to Linear Form x 8 9 (a) x is a solution. (b) x is not a solution x x (a) x is not a solution. (b) x 6 is not a solution. Section. Equations That Reduce to Linear Form x x x x t 5t 5 0 5t t 5 5t t 5 5 8x 9 9. x 5 8x x. z 6 8 z 6 8 z 8 z 8 z 0 z 0 z 0 0 Cengage Learning. All Rights Reserved. Ma not be scanned, copied or duplicated, or posted to a publicl accessible website, in whole or in part.