Algebra for College Students, 8th Edition Solution Manual

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Algebra for College Students, 8th Edition Solution Manual - Page 1 preview image

’SSOLUTIONSMANUALGEXPUBLISHINGSERVICESALGEBRA FORCOLLEGESTUDENTSEIGHTHEDITIONMargaret L. LialAmerican River CollegeJohn HornsbyUniversity of New OrleansTerry McGinnis

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Algebra for College Students, 8th Edition Solution Manual - Page 2 preview image

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Algebra for College Students, 8th Edition Solution Manual - Page 3 preview image

Table of ContentsRReview of the Real Number System.......................................................................................................1R.1R.2R.3R.4Basic Concepts • ................................................................................................................Operations on Real Numbers • ..........................................................................................Exponents, Roots, and Order of Operations • ....................................................................Properties of Real Numbers • ............................................................................................Chapter R Test •.................................................................................................................161220231Linear Equations, Inequalities, and Applications ............................................................................. 261.11.21.31.41.51.61.7Linear Equations in One Variable • ...................................................................................Formulas and Percent • ......................................................................................................Applications of Linear Equations •....................................................................................Further Applications of Linear Equations • .......................................................................Summary Exercises Applying Problem-Solving Techniques• ...........................................Linear Inequalities in One Variable • ................................................................................Set Operations and Compound Inequalities • ....................................................................Absolute Value Equations and Inequalities •.....................................................................Summary Exercises Solving Linear and Absolute Value Equationsand Inequalities• ....................................................................................................Chapter 1 Review Exercises •............................................................................................Chapter 1 Mixed Review Exercises • ................................................................................Chapter 1 Test • .................................................................................................................26374659687284921061101161192Linear Equations, Graphs, and Functions ....................................................................................... 1222.12.22.32.42.52.6Linear Equations in Two Variables •.................................................................................The Slope of a Line • .........................................................................................................Writing Equations of Lines• .............................................................................................Summary Exercises Finding Slopes and Equations of Lines•...........................................Linear Inequalities in Two Variables • ..............................................................................Introduction to Relations and Functions •..........................................................................Function Notation and Linear Functions •.........................................................................Chapter 2 Review Exercises •............................................................................................Chapter 2 Mixed Review Exercises • ................................................................................Chapter 2 Test • .................................................................................................................Chapters R−2 Cumulative Review Exercises •..................................................................122138151165168178185193199200203

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3Systems of Linear Equations ............................................................................................................. 2063.13.23.3Systems of Linear Equations in Two Variables • ..............................................................Systems of Linear Equations in Three Variables • ............................................................Applications of Systems of Linear Equations • .................................................................Chapter 3 Review Exercises •............................................................................................Chapter 3 Mixed Review Exercises • ................................................................................Chapter 3 Test • .................................................................................................................Chapters R−3 Cumulative Review Exercises •..................................................................2062272462652712732764Exponents, Polynomials, and Polynomial Functions....................................................................... 2814.14.24.34.44.5Integer Exponents and Scientific Notation •......................................................................Adding and Subtracting Polynomials •..............................................................................Polynomial Functions, Graphs, and Composition • ...........................................................Multiplying Polynomials •.................................................................................................Dividing Polynomials •......................................................................................................Chapter 4 Review Exercises •............................................................................................Chapter 4 Mixed Review Exercises • ................................................................................Chapter 4 Test • .................................................................................................................Chapters R−4 Cumulative Review Exercises •..................................................................2812953013123233343403423455Factoring ............................................................................................................................................. 3505.15.25.35.45.5Greatest Common Factors and Factoring by Grouping •.....................................................Factoring Trinomials •.........................................................................................................Special Factoring • ..............................................................................................................A General Approach to Factoring • .....................................................................................Solving Equations by the Zero-Factor Property •................................................................Chapter 5 Review Exercises • .............................................................................................Chapter 5 Mixed Review Exercises • ..................................................................................Chapter 5 Test •...................................................................................................................Chapters R−5 Cumulative Review Exercises •....................................................................350356364373380392397398400

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6Rational Expressions and Functions................................................................................................. 4046.16.26.36.46.56.6Rational Expressions and Functions; Multiplying and Dividing • ......................................Adding and Subtracting Rational Expressions •..................................................................Complex Fractions • ............................................................................................................Equations with Rational Expressions and Graphs •.............................................................Summary Exercises Simplifying Rational Expressions vs. SolvingRational Equations•.................................................................................................Applications of Rational Expressions • ...............................................................................Variation • ...........................................................................................................................Chapter 6 Review Exercises • .............................................................................................Chapter 6 Mixed Review Exercises • ..................................................................................Chapter 6 Test •...................................................................................................................Chapters R−6 Cumulative Review Exercises •....................................................................4044134264364494544694794854884927Roots, Radicals, and Root Functions ................................................................................................ 4987.17.27.37.47.57.67.7Radical Expressions and Graphs •.......................................................................................Rational Exponents • ...........................................................................................................Simplifying Radicals, the Distance Formula, and Circles •.................................................Adding and Subtracting Radical Expressions • ...................................................................Multiplying and Dividing Radical Expressions • ................................................................Summary Exercises Performing Operations with Radicals andRational Exponents• ................................................................................................Solving Equations with Radicals • ......................................................................................Complex Numbers • ............................................................................................................Chapter 7 Review Exercises • .............................................................................................Chapter 7 Mixed Review Exercies •....................................................................................Chapter 7 Test •...................................................................................................................Chapters R−7 Cumulative Review Exercises •....................................................................498505513525532543547558565573575578

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8Quadratic Equations, Inequalities, and Functions .......................................................................... 5838.18.28.38.48.5The Square Root Property and Completing the Square • ....................................................The Quadratic Formula • .....................................................................................................Equations Quadratic in Form • ............................................................................................Summary Exercises Applying MethodsforSolving Quadratic Equations•.........................Formulas and Further Applications •...................................................................................Polynomial and Rational Inequalities • ...............................................................................Chapter 8 Review Exercises • .............................................................................................Chapter 8 Mixed Review Exercises • ..................................................................................Chapter 8 Test •...................................................................................................................Chapters R−8 Cumulative Review Exercises •....................................................................5835986096346386526736816846899Additional Graphs of Functions and Relations ............................................................................... 6959.19.29.39.49.5Review of Operations and Composition • .........................................................................Graphs of Quadratic Functions • .......................................................................................More About Parabolas and Their Applications •...............................................................Symmetry; Increasing and Decreasing Functions • ...........................................................Piecewise Linear Functions • ............................................................................................Chapter 9 Review Exercises • ...........................................................................................Chapter 9 Mixed Review Exercises • ................................................................................Chapter 9 Test •.................................................................................................................Chapters R−9 Cumulative Review Exercises •..................................................................69570871773374375576176376610Inverse, Exponential, and Logarithmic Functions................................................................................ 77210.110.210.310.410.510.6Inverse Functions • ............................................................................................................Exponential Functions • ....................................................................................................Logarithmic Functions • ....................................................................................................Properties of Logarithms •.................................................................................................Common and Natural Logarithms •...................................................................................Exponential and Logarithmic Equations; Further Applications •......................................Chapter 10 Review Exercises • .........................................................................................Chapter 10 Mixed Review Exercises • ..............................................................................Chapter 10 Test •...............................................................................................................Chapters R−10 Cumulative Review Exercises •................................................................772782790802808813825832834836

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11Polynomial and Rational Functions.................................................................................................. 84211.111.211.311.4Zeros of Polynomial Functions (I) • ..................................................................................Zeros of Polynomial Functions (II) •.................................................................................Graphs and Applications of Polynomial Functions •.........................................................Summary Exercises Examining Polynomial Functions and Graphs•...............................Graphs and Applications of Rational Functions • .............................................................Chapter 11 Review Exercises • .........................................................................................Chapter 11 Mixed Review Exercises • ..............................................................................Chapter 11 Test •...............................................................................................................Chapters R−11 Cumulative Review Exercises •................................................................84284886088088690291191291512Conic Sections and Nonlinear Systems............................................................................................. 92212.112.212.312.4Circles Revisited and Ellipses •.........................................................................................Hyperbolas and Functions Defined by Radicals • .............................................................Nonlinear Systems of Equations • .....................................................................................Second-Degree Inequalities, Systems of Inequalities, and Linear Programming • ...........Chapter 12 Review Exercises • .........................................................................................Chapter 12 Mixed Review Exercises • ..............................................................................Chapter 12 Test •...............................................................................................................Chapters R−12 Cumulative Review Exercises •................................................................92293294395597698398498713Further Topics in Algebra ................................................................................................................. 99413.113.213.313.413.513.613.7Sequences and Series • ......................................................................................................Arithmetic Sequences • .....................................................................................................Geometric Sequences •......................................................................................................The Binomial Theorem • ...................................................................................................Mathematical Induction • ..................................................................................................Counting Theory • .............................................................................................................Basics of Probability • .......................................................................................................Chapter 13 Review Exercises • .........................................................................................Chapter 13 Mixed Review Exercises • ..............................................................................Chapter 13 Test •...............................................................................................................Chapters R−13 Cumulative Review Exercises •................................................................9941000100910201025103710441050105710591063

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Algebra for College Students, 8th Edition Solution Manual - Page 8 preview image

Chapter 1 Linear Equations, Inequalities, and Applications26Chapter 1Linear Equations, Inequalities, andApplications1.1Linear Equations in One VariableClassroom Examples, Now Try Exercises1.(a)9100x+=is anequationbecause itcontains an equals symbol.(b)910x+is anexpressionbecause it does notcontain an equals symbol.N1.(a)2173xx+−is anexpressionbecause itdoes not contain an equals symbol.(b)2173xx+=is anequationbecause itcontains an equals symbol.2.489171121710Combine terms.1217171017Subtract 17 .510Combine terms.510Divide by5.552xxxxxxxxxxxxx+= −+−=−−=−−−= −−−=−−−=Check by substituting 2 forxin the originalequation.???4891714(2)8(2)917(2)1Let2.8169341242512424Truexxxx+= −+−+= −+−=+= −+−=−=The solution set is{}2 .N2.511213351113Combine terms.51113Add.61113Combine terms.611111311Subtract 11.624Combine terms.624Divide by 6.664xxxxxxxxxxxxxxx+=−−+= −−++= −−++= −+−= −−= −−== −Check by substituting4−forxin the originalequation.???51121335( 4)112( 4)133( 4)Let4.2011813129211299Truexxxx+=−−−+=−−−−= −−+= −−+−= −+−= −The solution set is { 4}.−3.()3 45312353Distributive prop.12253Combine terms.1222532Subtract 2 .1233Combine terms.123333Add 3.153Combine terms.153Divide by 3.335xxxxxxxxxxxxxxxxxx+−=−+−=−+=−+−=−−=−+=−+===We will use the following notation to indicatethe value of each side of the original equationafter we have substituted the proposed solutionand simplified.Check5 :275253Truex=−=−The solution set is{}5 .N3.()541232xx−−=−5201232Distributive prop.53232Combine terms.5322322Add 2 .7323Combine terms.73232332Add 32.735Combine terms.735Divide by 7.775xxxxxxxxxxxxxx−−=−−=−−+=−+−=−+=+===We will use the following notation to indicatethe value of each side of the original equationafter we have substituted the proposed solutionand simplified.Check5 :512310Truex=−=−The solution set is{}5 .

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1.1 Linear Equations in One Variable274.6(4)82(35)648610Distributive prop.2210Combine terms.2210Add.2310Combine terms.21031010Add 10.123Combine terms.123Divide by 3.334xxxxxxxxxxxxxxxxxx−+=−+−−=−−−=−−+=−+=−+=−+===Check4 :23234Truex=−=−The solution set is{}4 .N4.()()23 26413626184436Dist. prop.418440Combine terms.4181844018Add 18 .42240Combine terms.440224040 Subtract 40.4422Combine terms.4422Divide by 22.22222xxxxxxxxxxxxxxxx−+=++−−=++−−=+−−+=++−=+−−=+−−=−=−=Check2 :230436Truex= −+= −+The solution set is{}2 .−5.Multiply each side by the LCD, 4, and use thedistributive property1312421314442422(1)1(3)2223235233Subtract 5.1Divide by 3.xxxxxxxxxxx+++=++⎛⎞⎛⎞⎛⎞+=⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠+++=+++=+== −= −Check211:0True42x= −+=The solution set is { 1}.−N5.Multiply each side by the LCD, 8, and use thedistributive property.424548424888(5)482(4)1(24)402824404440444Add 4.11Divide by 4.xxxxxxxxxxx−++=−+⎛⎞⎛⎞+=⎜⎟⎜⎟⎝⎠⎝⎠−++=−++=−===Check71311:5True44x=+=The solution set is{}11 .6.Multiply each term by 100.0.02(60)0.040.03(50)2(60)43(50)12041503430330xxxxxxxxx+=++=++=+=+=Check30 :1.21.22.4Truex=+=The solution set is{}30 .N6.Multiply each term by 100.0.080.12(4)0.03(5)812(4)3(5)8124831544831546336379xxxxxxxxxxxxxxx−−=−−−=−−+=−−+=−−+===Check9 :0.720.600.12Truex=−=The solution set is{}9 .7.(a)5(2)2(1)315102231383138331381Falsexxxxxxxxxxxx+−+=++−−=++=++−=+−=Since the result,81,=isfalse,the equationhas no solution and is called acontradiction.The solution set is.∅

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Chapter 1 Linear Equations, Inequalities, and Applications28(b)Multiply each side by the LCD, 3, and usethe distributive property.12133312133333312313131xxxxxxxxxxx++=++⎛⎞⎛⎞⎛⎞+=+⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠++=++=+This is anidentity.Any real number willmake the equation true.The solution set is {all real numbers}.(c)5(31)515551455Subtract.140Subtract 5.0Divide by 14.xxxxxxxx+=++=++===This is aconditional equation.Check0 :5(1)05Truex==+The solution set is{}0 .N7.(a)93(4)6(2)9312612612612xxxxxxxx−+=−−−=−−=−This is anidentity.Any real number willmake the equation true.The solution set is{}all real numbers .(b)3(21)236323833933Subtract.90Subtract 3.0Divide by9.xxxxxxxxxxxx−−−=+−+−=+−+=+−+=−==−This is aconditional equation.Check0 :3( 1)3Truex=−−=The solution set is{}0 .(c)10212(5)810212108102110101021101010102110Falsexxxxxxxxxxxx−=−+−=−+−=−−−=−−−= −Since the result,2110,−= −isfalse,theequation has no solution and is called acontradiction.The solution set is.∅Exercises1.A collection of numbers, variables, operationsymbols, and grouping symbols, such as()2 815 ,x−is an algebraic expression. Whilean equationdoesinclude an equality symbol,thereis notan equality symbol in an algebraicexpression.2.A linear equation in one variable (herex) canbe written in the form,AxBC+=with0.A≠Another name for a linear equation is afirst-degree equation, because the greatestpower on the variable isone.3.If we let2x=in the linear equation259,x+=atruestatement results. Thenumber 2 is a solution of the equation, and{}2is the solution set.4.A linear equation with one solution in itssolution set, such as the equation in Exercise 3,is a conditional equation.5.A linear equation with an infinite number ofsolutions is an identity. Its solution set is{}all real numbers .6.A linear equation with no solution is acontradiction. Its solution set is theempty set.∅7.320xx+−=can be written as 42,x=so it islinear.949x−=is in linear form.Choices A and C are linear.8.212x=is not a linear equation because thevariable is squared.1108xx−=is not a linear equation becausethere is a variable in the denominator of thesecond term.Choices B and D are nonlinear.9.??3(4)5Original equation3(64)5 6Let6.3(10)30Add.3030Truexxx+=+=⋅===Since a true statement is obtained, 6 is asolution.

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1.1 Linear Equations in One Variable2910.???5(4)3(6)9(1)5( 24)3( 26)9( 21)Let2.5(2)3(4)9( 1)Add.10129Multiply.29Falsexxxx+−+=+−+−−+=−+= −−=−−= −−= −Since a false statement is obtained,2−is not asolution.11.324xx−+−=is anequationbecause itcontains an equals symbol.12.3244xx−+−−=is anequationbecause itcontains an equals symbol.13.4(3)2(1)10xx+−+−is anexpressionbecauseit does not contain an equals symbol.14.4(3)2(1)10xx+−++is anexpressionbecauseit does not contain an equals symbol.15.101243xx−+−= −is anequationbecause itcontains an equals symbol.16.1012430xx−+−+=is anequationbecause itcontains an equals symbol.17.A sign error was made when the distributiveproperty was applied. The left side of thesecond line should be846.xx−+()82 233784637Distributive property4637Combine like terms.1Subtract 3and 6.xxxxxxxxxx−−=+−+=++=+=The correct solution is 1.18.The negative sign−represents1.−()52455245Distributive property79Combine terms.xxxxx−−−+= −−++= −+19.78178818Subtract 8.7777Divide by 7.771xxxxx+=+−=−= −−== −We will use the following notation to indicatethe value of each side of the original equationafter we have substituted the proposed solutionand simplified.Check1:781Truex= −−+=The solution set is { 1}.−20.5421544214Add 4.525525Divide by 5.555xxxxx−=−+=+===Check5 :25421Truex=−=The solution set is{}5 .21.5236523363Subtract 3 .22622262Subtract 2.2828Divide by 2.224xxxxxxxxxxxx+=−+−=−−+= −+−= −−= −−== −Check4 :202126Truex= −−+= −−The solution set is { 4}.−22.9179917797Subtract 7 .21921191Subtract 1.210210Divide by 2.225xxxxxxxxxxxx+=−+−=−−+= −+−= −−= −−== −Check5 :451359Truex= −−+= −−The solution set is { 5}.−23.751582158Combine terms.27Subtract 15.7Subtract.xxxxxxxxx−+=++=+=−= −Check7 :49351578Truex= −−++= −+The solution set is { 7}.−

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Chapter 1 Linear Equations, Inequalities, and Applications3024.2445445Combine terms.345Subtract 4 .39Subtract 4.3Divide by3.xxxxxxxxx+−=−+=−−+= −−= −=−Check3 :643125Truex=+−=−The solution set is{}3 .25.12159535927434Combine terms.3044.Add 3.300Add 4.0Divide by 30.wwwwwwwww+−+= −+−−= −−−= −==Check0 :9559Truew=−+=−The solution set is{}0 .26.458464464Combine terms.544Subtract 6 .50Add 4.0Divide by5.xxxxxxxxx−+−+=−−=−−−= −−==−Check0 :844Truex=−+= −The solution set is {0}.27.3(24)202612202Distributive property81220Add 2 .832Add 12.4Divide by 8.tttttttt−=−−=−−===Check4 :3(4)208Truet==−The solution set is{}4 .28.2(32 )4644Distributive property654Subtract.510Subtract 6.2Divide by5.xxxxxxxx−=−−=−−= −−= −=−Check2 :2( 1)24Truex=−=−The solution set is{}2 .29.5(1)3264553264Distributive prop.2364Combine terms.384Add 2 .78Subtract 4.7Divide by 8.8xxxxxxxxxxxx−+++=+−−++=+−−=+−=+−=−=Check:Substitute78−forxand show that bothsides equal1.25.−The screen shows a typicalCheck on a calculator.The solution set is7.8⎧⎫−⎨⎬⎩⎭30.5(3)45425154542Distributive prop.91042Combine terms.11104Add 2 .116Subtract 10.6Divide by 11.11xxxxxxxxxxxx++−=−++−=−+=−+== −= −Check6 :1113524554412True1111111111x= −−−=+The solution set is6.11⎧⎫−⎨⎬⎩⎭31.2593(4)539312539317917Falsexxxxxxx−+−=−−−=−−−=−−= −The equation is acontradiction.The solution set is.∅32.62112(23)44114644114101110Falsexxxxxxx−+−= −−+−−= −++−−= −+−=The equation is acontradiction.The solution set is.∅

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1.1 Linear Equations in One Variable3133.2(3)4(1)2644Remove parentheses.664Add 4x.610Subtract 6.105Divide by6.63xxxxxxx+= −++= −−+= −= −−== −−Check542:24True333x⎛⎞⎛⎞= −= −−⎜⎟⎜⎟⎝⎠⎝⎠The solution set is5.3⎧⎫−⎨⎬⎩⎭34.4(9)8(3)436824Remove parentheses.43624Subtract 8 .460Add 36.15Divide by4.xxxxxxxx−=+−=+−−=−== −−Check15 :4( 24)8( 12)Truex= −−=−The solution set is { 15}.−35.3(21)2(2)563245475422142xxxxxxx+−−=+−+=+== −−== −Check15:3(0)25True22x⎛⎞= −−−=⎜⎟⎝⎠The solution set is1.2⎧⎫−⎨⎬⎩⎭36.4(2)2(3)648266626688463xxxxxxx−++=−++=−====Check4213:426True333x⎛⎞⎛⎞=−+=⎜⎟⎜⎟⎝⎠⎝⎠The solution set is4.3⎧⎫⎨⎬⎩⎭37.23(4)2(3)2312265122636623xxxxxxxxxx+−=−+−=−−=−===Check2 :43( 2)2( 1)Truex=+−=−The solution set is {2}.38.63(52)4(1)61564496445101025xxxxxxxxxx−+=−−−=−−−=−−=== −−Check2 :123( 8)4(3)Truex= −−−−=The solution set is { 2}.−39.64(32 )5(4)1061285201014125309182xxxxxxxxxx−−=−−−+=−−−=−= −= −Check2 :124(7)5( 6)10Truex= −−−=−−The solution set is { 2}.−40.23(42 )2(3)2212626241224284xxxxxxxxxx−−−=−+−−+=−+−=−==Check4 :83( 4)2(1)2Truex=−−−=+The solution set is {4}.41.2(3)43(4)22643122310310xxxxxxxx−+−−= −++−−−−= −−+−−= −−The equation is anidentity.The solution set is {all real numbers}.42.4(27)2253(21)82822563828828xxxxxxxx+=++++=++++=+The equation is anidentity.The solution set is {all real numbers}.

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Chapter 1 Linear Equations, Inequalities, and Applications3243.2[(24)3]2(1)2[243]2(1)2[1]2(1)11Divide by 2.121Add.22Subtract 1.1Divide by 2.xxxxxxxxxxxxxx−++=+−−+=+−−=+−−=+−=+−=−=Check1:2[ 123]0Truex= −− −+=The solution set is { 1}.−44.4[2(3)5](27 )4[235](27 )4[32](27 )128271982Add 7 .1910Subtract 8.10Divide by 19.19xxxxxxxxxxxxxx−−+= −+−++= −++= −++= −−+= −= −= −Check10 :19206795324True19191919x= −⎡⎤⎛⎞−−+= −−⎜⎟⎢⎥⎣⎦⎝⎠The solution set is10.19⎧⎫−⎨⎬⎩⎭45.[2(52)]2(27)[252]227[ 32]22732297xxxxxxxxxxx−−+=++−−−=++− −−=+++=+=Check7 :[1437]221Truex=−−=+The solution set is {7}.46.[6(48)]9(63)[648]963(28)61228612844182xxxxxxxxxxxx−−+=++−−−=++−−=+−+=+−=== −−Check1 :[ 36]90True2x= −− −−=+The solution set is1.2⎧⎫−⎨⎬⎩⎭47.365(1)5(24)5365552458117922xxxxxxxxxxxx−+−−= −−−+−+−+= −−++−+= −+−= −=Check2 :6651005Truex=−+−= −−+The solution set is {2}.48.4(2)85392(6)48853921243536xxxxxxxxxxx+−−= −+−++−−= −+−−−+= −−= −Check6 :164851890Truex= −−+−=+−The solution set is { 6}.−49.7[2(34 )]292(115 )7[234 ]292307[ 14 ]27307282730730730xxxxxxxxxxxxxx−+−= −+−−−−= −+−− −−= −−−−−= −−−−= −−The equation is anidentity.The solution set is {all real numbers}.50.4[6(12 )]102(103 )84[612 ]1020684(52 )1020220810202202202xxxxxxxxxxxxxxxx−++=−+−−+=−+−+=+−+=++=+The equation is anidentity.The solution set is {all real numbers}.51.[3(25)]4[3(24)3 ][325]4[6123 ][5]4[312]543125382332xxxxxxxxxxxxxxxx−−+= −−−−−−−= −−−−−−= −−−−+= −−+−+= −+==

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Algebra for College Students, 8th Edition Solution Manual - Page 15 preview image

1.1 Linear Equations in One Variable33Check3 :299843True22x=⎡⎤⎡⎤−−= −−−−⎢⎥⎢⎥⎣⎦⎣⎦The solution set is3.2⎧⎫⎨⎬⎩⎭52.2[ (1)4]5[ (67)9 ]2[14]5[ 679 ]2[5]5[37]2103125225xxxxxxxxxxxx−−+=+ −−+−++=+ −++−+=++−+=+−== −Check2 :574718245True555x= −⎡⎤⎡⎤+=+−⎢⎥⎢⎥⎣⎦⎣⎦The solution set is2.5⎧⎫−⎨⎬⎩⎭53.The denominators of the fractions are 3, 4, 6,and 1. The least common denominator is 12since it is the smallest number into which eachdenominator can divide without a remainder.54.Yes, the coefficients will be larger, but you willget the correct solution. As long as youmultiply both sides of the equation by thesamenonzero number, the resulting equation isequivalent and the solution does not change.55.(a)We need to make 0.04, 0.06, 0.03, and 1.46integers. These numbers can be written as4,1006,1003,100and 146 ,100respectively.Multiplying by210 ,or 100, will eliminatethe decimal points (the denominators) sothat all the coefficients are integers.(b)We need to make 0.006, 0.02, 0.03, 0.008,and 0.25 integers. These numbers can bewritten as6,10002,1003,1008,1000and25 ,100respectively.Multiplying by310 , or1000, will eliminate the decimal points (thedenominators) so that all the coefficients areintegers.56.0.06(10)(100)0.06(100)(10)6(10)606Choice B is correct.xxxx−=−=−=−57.529518Multiply by 9.1818Divide by5.55xxx−=−=== −−−Check18518:2True595x⎛⎞ ⎛⎞= −−−=⎜⎟ ⎜⎟⎝⎠ ⎝⎠The solution set is18.5⎧⎫−⎨⎬⎩⎭58.3511355Multiply by 11.5555Divide by 3.33xxx= −= −−== −Check55355:5True3113x⎛⎞⎛⎞= −−= −⎜⎟⎜⎟⎝⎠⎝⎠The solution set is55.3⎧⎫−⎨⎬⎩⎭59.61565Multiply by 5.55Divide by 6.66xxx= −= −−== −Check565:1True656x⎛⎞⎛⎞= −−= −⎜⎟⎜⎟⎝⎠⎝⎠The solution set is5.6⎧⎫−⎨⎬⎩⎭60.768748Multiply by 8.4848Divide by7.77xxx−=−=== −−−Check48748:6True787x⎛⎞⎛⎞= −−−=⎜⎟⎜⎟⎝⎠⎝⎠The solution set is48.7⎧⎫−⎨⎬⎩⎭

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Algebra for College Students, 8th Edition Solution Manual - Page 16 preview image

Chapter 1 Linear Equations, Inequalities, and Applications3461.Multiply both sides by the LCD, 6.52366(5)236630Distributive property233230530Add.6Divide by 5.xxxxxxxxxx+=⎛⎞+=⎜⎟⎝⎠⎛⎞⎛⎞+=⎜⎟⎜⎟⎝⎠⎝⎠+===Check6 :325Truex=+=The solution set is {6}.62.Multiply both sides by the LCD, 20.1542020(1)54202020Distributive property54452020Subtract.20Multiply by1.xxxxxxxxxx−=⎛⎞−=⎜⎟⎝⎠⎛⎞⎛⎞−=⎜⎟⎜⎟⎝⎠⎝⎠−=−== −−Check20 :451Truex= −−+=The solution set is { 20}.−63.Multiply both sides by the LCD, 4.3513423544(13)4235444(13) Distributive prop.42310521352Combine terms.4Divide by 13.xxxxxxxxxx+=⎛⎞+=⎜⎟⎝⎠⎛⎞⎛⎞+=⎜⎟⎜⎟⎝⎠⎝⎠+===Check4 :31013Truex=+=The solution set is {4}.64.Multiply both sides by the LCD, 6.81332866( 13)328666( 13)Distributive prop.321637813786Divide by 26.xxxxxxxxxx−= −⎛⎞−=−⎜⎟⎝⎠⎛⎞⎛⎞−=−⎜⎟⎜⎟⎝⎠⎝⎠−= −= −= −Check6 :16313Truex= −−+= −The solution set is { 6}.−65.Multiply both sides by the LCD, 6.10255310215155533(10)3(2)5330658242438xxxxxxxxxx−+= −−⎛⎞⎛⎞+=−⎜⎟⎜⎟⎝⎠⎝⎠−+= −−+= −===Check723 :1True55x=−+= −The solution set is {3}.66.Multiply both sides by the LCD, 54.()()55665455545466549 59 545945990901090910xxxxxxxxxxxx−+=−⎛⎞⎛⎞+=⎜⎟⎜⎟⎝⎠⎝⎠−+=−+=−+====Check364599 :True545454x−=+=The solution set is {9}.

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