Chapter 7 - XYZ Custom Plus

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438<strong>Chapter</strong> 7 Solving Equations57. MP 3 Players Southwest Electronics tracked the numberof MP 3 players it sold each month for a year. The storemanager found that when he raised the price of theMP 3 players just slightly, sales went down. He usedthe equation 60 = −2x + 130 to determine the price xhe needs to charge if he wants to sell 60 MP 3 players amonth. Solve this equation.$35.0058. Part-time Tuition Costs Many two-year colleges havea large number of students who take courses on apart-time basis. Students pay a charge for each credithour taken plus an activity fee. Suppose the equation$1960 = $175x + $35 can be used to determine the numberof credit hours a student is taking during the upcomingsemester. Solve this equation.11 credit hours59. Super Bowl XLII According to Nielsen Media Research,the New York Giants’ victory over the New EnglandPatriots in Super Bowl XLII was the most watchedSuper Bowl ever, with 3 million more viewers thanthe previous record for Super Bowl XXX in 1996. Theequation 192,000,000 = 2x − 3,000,000 shows that thetotal number of viewers for both Super Bowl gameswas 192 million. Solve for x to determine how manyviewers watched Super Bowl XLII.97,500,000 or 97.5 million viewers60. Blending Gasoline In an attempt to save money at thegas pump, customers will combine two different octanegasolines to get a blend that is slightly higher in octanethan regular gas but not as expensive as premium gas.The equation 14x + 120 − 6x = 200 can be used to findout how many gallons of one octane are needed. Solvethis equation.10 gallonsOCTANE1OCTANEBLENDOCTANE214x + 120 − 6x = 200192,000,000 viewers totalMaintaining Your SkillsTranslations Translate each sentence below into an equation, then solve the equation.61. The sum of 2x and 5 is 19.2x + 5 = 19; x = 762. The sum of 8 and 3x is 2.8 + 3x = 2; x = −263. The difference of 5x and 6 is −9.64. The difference of 9 and 6x is 21._5x − 6 = −9; x = − 3 5 9 − 6x = 21; x = −2Getting Ready for the Next SectionApply the distributive property to each of the following expressions.65. 2(3a − 8)66. 4(2a − 5)67. −3(5x − 1)68. −2(7x − 3)6a − 168a − 20−15x + 3−14x + 6Simplify each of the following expressions as much as possible.69. 3(y − 5) + 670. 5(y + 3) + 771. 6(2x − 1) + 4x72. 8(3x − 2) + 4x3y − 95y + 2216x − 628x − 16
Introduction . . .The Rhind Papyrus is an ancientEgyptian document, created around1650 bc, that contains some mathematicalriddles. One problem on the RhindPapyrus asked the reader to find a quantitysuch that when it is added to onefourthof itself the sum is 15. The equationthat describes this situation isLinear Equations in One Variablex + _1 x = 154As you can see, this equation containsa fraction. One of the topics we will discuss in this section is how to solve equationsthat contain fractions.In this chapter we have been solving what are called linear equations in onevariable. They are equations that contain only one variable, and that variable isalways raised to the first power and never appears in a denominator. Here aresome examples of linear equations in one variable:3x + 2 = 17, 7a + 4 = 3a − 2, 2(3y − 5) = 6Because of the work we have done in the first three sections of this chapter, weare now able to solve any linear equation in one variable. The steps outlinedbelow can be used as a guide to solving these equations.ASolving Linear Equations with One VariableStrategyExample 1Solve: 3(x + 2) = −9SolutionSolving a Linear Equation with One VariableStep 1: Simplify each side of the equation as much as possible. This step isdone using the commutative, associative, and distributive properties.Step 2: Use the addition property of equality to get all variable terms on oneside of the equation and all constant terms on the other, and thencombine like terms. A variable term is any term that contains the variable.A constant term is any term that contains only a number.Step 3: Use the multiplication property of equality to get the variable by itselfon one side of the equation.Step 4: Check your solution in the original equation if you think it is necessary.We begin by applying the distributive property to the left side:Step 1Step 2Step 3{{{Bridgeman Art Library/Getty Images3(x + 2) = −93x + 6 = −93x + 6 + (−6) = −9 + (−6)3x = −15Distributive propertyAdd −6 to both sidesAddition_3x = −15_3 3Divide both sides by 3x = −5Division7.4 Linear Equations in One Variable7.4ObjectivesA Solve linear equations with onevariable.B Solve linear equations involvingfractions and decimals.NoteOnce you have somepractice at solvingequations, these stepswill seem almost automatic. Untilthat time, it is a good idea to payclose attention to these steps.Instructor NoteUsing division on the last step insolving equations is always shownin the examples in this section. However,if I were working Example 1 inclass, when I reached the last stepI would say, “We can multiply bothsides by 1/3 or we can divide bothsides by 3,” just to remind them thatthe two processes are equivalent.Practice Problems1. Solve: 4(x + 3) = −8Answer1. −5439
Page 1 and 2: Solving Equations7IntroductionImage
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Page 76: RESEARCH PROJECTAlgebraic Symbolism

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