Chapter 9 - XYZ Custom Plus

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538 <strong>Chapter</strong> 9 Solving Equations and Inequalities 57. MP3 Players Southwest Electronics tracked the number of MP3 players it sold each month for a year. The store manager found that when he raised the price of the MP3 players just slightly, sales went down. He used the equation 60 5 22x 1 130 to determine the price x he needs to charge if he wants to sell 60 MP3 players a month. Solve this equation. 58. Part-time Tuition Costs Many two-year colleges have a large number of students who take courses on a part-time basis. Students pay a charge for each credit hour taken plus an activity fee. Suppose the equation $1960 5 $175x 1 $35 can be used to determine the number of credit hours a student is taking during the upcoming semester. Solve this equation. 59. Super Bowl XLII According to Nielsen Media Research, the New York Giants’ victory over the New England Patriots in Super Bowl XLII was the most watched Super Bowl ever, with 3 million more viewers than the previous record for Super Bowl XXX in 1996. The equation 192,000,000 5 2x 2 3,000,000 shows that the total number of viewers for both Super Bowl games was 192 million. Solve for x to determine how many viewers watched Super Bowl XLII. 60. Blending Gasoline In an attempt to save money at the gas pump, customers will combine two different octane gasolines to get a blend that is slightly higher in octane than regular gas but not as expensive as premium gas. The equation 14x 1 120 2 6x 5 200 can be used to find out how many gallons of one octane are needed. Solve this equation. OCTANE 1 OCTANE BLEND OCTANE 2 192,000,000 viewers total 14x + 120 ‒ 6x = 200 Maintaining Your Skills Translations Translate each sentence below into an equation, then solve the equation. 61. The sum of 2x and 5 is 19. 62. The sum of 8 and 3x is 2. 63. The difference of 5x and 6 is 29. 64. The difference of 9 and 6x is 21. Getting Ready for the Next Section Apply the distributive property to each of the following expressions. 65. 2(3a 2 8) 66. 4(2a 2 5) 67. 23(5x 2 1) 68. 22(7x 2 3) Simplify each of the following expressions as much as possible. 69. 3(y 2 5) 1 6 70. 5(y 1 3) 1 7 71. 6(2x 2 1) 1 4x 72. 8(3x 2 2) 1 4x
Introduction . . . Linear Equations in One Variable The Rhind Papyrus is an ancient Egyptian document, created around 1650 bc, that contains some mathematical riddles. One problem on the Rhind Papyrus asked the reader to find a quantity such that when it is added to one-fourth of itself the sum is 15. The equation that describes this situation is x 1 }} 1 4 }x x 5 15 As you can see, this equation contains a fraction. One of the topics we will discuss in this section is how to solve equations that contain fractions. In this chapter we have been solving what are called linear equations in one variable. They are equations that contain only one variable, and that variable is always raised to the first power and never appears in a denominator. Here are some examples of linear equations in one variable: 3x 1 2 5 17, 7a 1 4 5 3a 2 2, 2(3y 2 5) 5 6 Because of the work we have done in the first three sections of this chapter, we are now able to solve any linear equation in one variable. The steps outlined below can be used as a guide to solving these equations. Bridgeman Art Library/Getty Images 9.4 Objectives A Solve linear equations with one variable. b Solve linear equations involving fractions and decimals. C Solve application problems using linear equations in one variable. Examples now playing at MathTV.com/books A Solving Linear Equations with One variable Strategy Solving a Linear Equation with One Variable Step 1: Simplify each side of the equation as much as possible. This step is done using the commutative, associative, and distributive properties. Step 2: Use the addition property of equality to get all variable terms on one side of the equation and all constant terms on the other, and then combine like terms. A variable term is any term that contains the variable. A constant term is any term that contains only a number. Note Once you have some practice at solving equations, these steps will seem almost automatic. Until that time, it is a good idea to pay close attention to these steps. Step 3: Use the multiplication property of equality to get the variable by itself on one side of the equation. Step 4: Check your solution in the original equation if you think it is necessary. ExAmplE 1 Solve: 3(x 1 2) 5 29 SOlutiOn We begin by applying the distributive property to the left side: Step 1 Step 2 Step 3 5 5 5 3(x 1 2) 5 29 3x 1 6 5 29 Distributive property 3x 1 6 1 (−6) 5 29 1 (−6) Add 26 to both sides 3x 5 215 Addition } 3x x 215 } 5 }} Divide both sides by 3 3 3 x 5 25 Division prACtiCE prOblEmS 1. Solve: 4(x 1 3) 5 28 Answer 1. 25 9.4 Linear Equations in One Variable 539
Page 1 and 2: Solving Equations and Inequalities
Page 3 and 4: The Distributive Property and Algeb
Page 5 and 6: 9.1 The Distributive Property and A
Page 7 and 8: 9.1 The Distributive Property and A
Page 9 and 10: 9.1 Problem Set 517 Problem Set 9.1
Page 11 and 12: 9.1 Problem Set 519 Find the value
Page 13 and 14: 9.1 Problem Set 521 91. Temperature
Page 15 and 16: Introduction . . . The Addition Pro
Page 17 and 18: 9.2 The Addition Property of Equali
Page 21 and 22: 9.2 Problem Set 529 Applying the Co
Page 23 and 24: The Multiplication Property of Equa
Page 25 and 26: 9.3 The Multiplication Property of
Page 29: 9.3 Problem Set 537 Find the value
Page 33 and 34: 9.4 Linear Equations in One Variabl
Page 37 and 38: 9.4 Problem Set 545 C Applying the
Page 39 and 40: Introduction . . . Applications As
Page 41 and 42: 9.5 Applications 549 Step 2 Assign
Page 43 and 44: 9.5 Applications 551 Example 4 The
Page 45 and 46: 9.5 Applications 553 Step 2 Assign
Page 49 and 50: 9.5 Problem Set 557 Coin Problems 3
Page 51 and 52: Introduction . . . Evaluating Formu
Page 53 and 54: 9.6 Evaluating Formulas 561 The rat
Page 57 and 58: 9.6 Problem Set 565 B Maximum Heart
Page 59 and 60: 9.6 Problem Set 567 Applying the Co
Page 61 and 62: Chapter 9 Summary Combining Similar
Page 63 and 64: Chapter 9 Review Simplify the expre
Page 65 and 66: Chapter 9 Cumulative Review 573 28.
Page 67 and 68: Chapter 9 Projects Solving Equation

Chapter 9 - XYZ Custom Plus

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