Solution Manual for Beginning and Intermediate Algebra, 6th Edition

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’SSOLUTIONSMANUALGEXPUBLISHINGSERVICESBEGINNING ANDINTERMEDIATEALGEBRASIXTHEDITIONMargaret L. LialAmerican River CollegeJohn HornsbyUniversity of New OrleansTerry McGinnis

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Table of ContentsRPrealgebra Review..................................................................................................................1R.1R.2Fractions •.................................................................................................................Decimals and Percents • ...........................................................................................1151The Real Number System ......................................................................................................261.11.21.31.41.51.61.7Exponents, Order of Operations, and Inequality •....................................................Variables, Expressions, and Equations • ..................................................................Real Numbers and the Number Line •......................................................................Adding and Subtracting Real Numbers • .................................................................Multiplying and Dividing Real Numbers •...............................................................Summary Exercises Performing Operations with Real Numbers• ..........................Properties of Real Numbers • ...................................................................................Simplifying Expressions • ........................................................................................Chapter 1 Review Exercises • ..................................................................................Chapter 1 Mixed Review Exercises • .......................................................................Chapter 1 Test •........................................................................................................26324044546365738085862Linear Equations and Inequalities in One Variable ............................................................892.12.22.32.42.52.62.72.8The Addition Property of Equality • .......................................................................The Multiplication Property of Equality •...............................................................More on Solving Linear Equations • .......................................................................Summary Exercises Applying Methods for Solving Linear Equations•..................Applications of Linear Equations • .........................................................................Formulas and Additional Applications from Geometry •........................................Ratio, Proportion, and Percent • ..............................................................................Further Applications of Linear Equations •.............................................................Solving Linear Inequalities • ...................................................................................Chapter 2 Review Exercises • .................................................................................Chapter 2 Mixed Review Exercises • ......................................................................Chapter 2 Test •.......................................................................................................Chapters R–2 Cumulative Review Exercises •........................................................89981061191221381491601721871931951973Linear Equations and Inequalities in Two Variables ............................................................2003.13.23.33.43.5Linear Equations and Rectangular Coordinates •....................................................Graphing Linear Equations in Two Variables • ......................................................The Slope of a Line •...............................................................................................Slope-Intercept Form of a Linear Equation • ..........................................................Point-Slope Form of a Linear Equation and Modeling • .........................................Summary Exercises Applying Graphing and Equation-Writing Techniquesfor Lines• ........................................................................................................Chapter 3 Review Exercises • .................................................................................Chapter 3 Mixed Review Exercises • ......................................................................Chapter 3 Test •.......................................................................................................Chapters R–3 Cumulative Review Exercises •........................................................200212230239251260264269271273

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4Exponents and Polynomials ....................................................................................................2764.14.24.34.44.54.64.7The Product Rule and Power Rules for Exponents •................................................Integer Exponents and the Quotient Rule • ..............................................................Summary Exercises Applying the Rules for Exponents•..........................................Scientific Notation • .................................................................................................Adding, Subtracting, and Graphing Polynomials • ..................................................Multiplying Polynomials • .......................................................................................Special Products •.....................................................................................................Dividing Polynomials • ............................................................................................Chapter 4 Review Exercises • ..................................................................................Chapter 4 Mixed Review Exercises • .......................................................................Chapter 4 Test •........................................................................................................Chapters R–4 Cumulative Review Exercises •.........................................................2762832912953043173273353503563583615Factoring and Applications.......................................................................................................3645.15.25.35.45.55.6The Greatest Common Factor; Factoring by Grouping • ........................................Factoring Trinomials • ............................................................................................More on Factoring Trinomials •..............................................................................Special Factoring Techniques •...............................................................................Summary Exercises Recognizing and Applying Factoring Strategies• ..................Solving Quadratic Equations Using the Zero-Factor Property • .............................Applications of Quadratic Equations •....................................................................Chapter 5 Review Exercises •.................................................................................Chapter 5 Mixed Review Exercises •........................................................................Chapter 5 Test • ......................................................................................................Chapters R–5 Cumulative Review Exercises • .......................................................3643723813934054094204304354374396Rational Expressions and Applications ...................................................................................4426.16.26.36.46.56.66.7The Fundamental Property of Rational Expressions •............................................Multiplying and Dividing Rational Expressions •..................................................Least Common Denominators • .............................................................................Adding and Subtracting Rational Expressions •.....................................................Complex Fractions •...............................................................................................Solving Equations with Rational Expressions • .....................................................Summary Exercises Simplifying Rational Expressions vs. SolvingRational Equations•.........................................................................................Applications of Rational Expressions •..................................................................Chapter 6 Review Exercises • ................................................................................Chapter 6 Mixed Review Exercises •.....................................................................Chapter 6 Test •......................................................................................................Chapters R–6 Cumulative Review Exercises •.......................................................442455465475492507529532544550553556

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7Graphs, Linear Equations, and Systems .................................................................................5627.17.27.37.47.57.67.7Review of Graphs and Slopes of Lines •................................................................Review of Equations of Lines; Linear Models• ....................................................Solving Systems of Linear Equations by Graphing • .............................................Solving Systems of Linear Equations by Substitution •.........................................Solving Systems of Linear Equations by Elimination • .........................................Summary Exercises Applying Techniques for Solving Systems of LinearEquations• .....................................................................................................Systems of Linear Equations in Three Variables•.................................................Applications of Systems of Linear Equations •......................................................Chapter 7 Review Exercises • ................................................................................Chapter 7 Mixed Review Exercises •.....................................................................Chapter 7 Test •......................................................................................................Chapters R–7 Cumulative Review Exercises •.......................................................5625815966076186286346536736846866918Inequalities and Absolute Value...............................................................................................6968.18.28.38.4Review of Linear Equations in One Variable • ......................................................Set Operations and Compound Inequalities •.........................................................Absolute Value Equations and Inequalities • .........................................................Summary Exercises Solving Linear and Absolute Value Equations andInequalities•...................................................................................................Linear Inequalities in Two Variables •...................................................................Chapter 8 Review Exercises • ................................................................................Chapter 8 Mixed Review Exercises •.....................................................................Chapter 8 Test •......................................................................................................Chapters R–8 Cumulative Review Exercises •.......................................................6967057127277317447477497519Relations and Functions ............................................................................................................7569.19.29.39.4Introduction to Relations and Functions • ..............................................................Function Notation and Linear Functions • .............................................................Polynomial Functions, Operations, and Composition •..........................................Variation • ..............................................................................................................Chapter 9 Review Exercises • ................................................................................Chapter 9 Mixed Review Exercises •.....................................................................Chapter 9 Test •......................................................................................................Chapters R–9 Cumulative Review Exercises •.......................................................756762770782792795796797

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10Roots, Radicals, and Root Functions .......................................................................................80310.110.210.310.410.510.610.7Radical 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 10 Review Exercises • ..............................................................................Chapter 10 Mixed Review Exercises •...................................................................Chapter 10 Test •....................................................................................................Chapters R−10 Cumulative Review Exercises • ....................................................80381382183484085285586787488288488711Quadratic Equations, Inequalities, and Functions ..............................................................89211.111.211.311.411.511.611.711.8Solving Quadratic Equations by the Square Root Property • ...................................Solving Quadratic Equations by Completing the Square •.......................................Solving Quadratic Equations by the Quadratic Formula • .......................................Solving Equations Quadratic in Form •....................................................................Summary Exercises Applying Methods for Solving Quadratic Equations •.............Formulas and Further Applications • .......................................................................Graphs of Quadratic Functions • ..............................................................................More About Parabolas and Their Applications •......................................................Polynomial and Rational Inequalities • ....................................................................892901920931956961975984999Chapter 11 Review Exercises • ..............................................................................Chapter 11 Mixed Review Exercises • ...................................................................Chapter 11 Test •....................................................................................................Chapters R–11 Cumulative Review Exercises •.....................................................102110321036104112Inverse, Exponential, and Logarithmic Functions................................................................104712.112.212.312.412.512.6Inverse Functions •..................................................................................................Exponential Functions • ..........................................................................................Logarithmic Functions •..........................................................................................Properties of Logarithms • ......................................................................................Common and Natural Logarithms • ........................................................................Exponential and Logarithmic Equations; Further Applications .............................Chapter 12 Review Exercises • ...............................................................................Chapter 12 Mixed Review Exercises • ....................................................................Chapter 12 Test •.....................................................................................................Chapters R–12 Cumulative Review Exercises •......................................................1047105710651077108310881100110711091111

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Chapter 1 The Real Number System26Chapter 1The Real Number System1.1 Exponents, Order of Operations, andInequalityClassroom Examples, Now Try Exercises1.(a)298199=⋅=(b)41111161 is us1ed as a factor 4 times.2122222⎛⎞⋅⋅=⎠=⎜⎟⎝⋅N1.(a)266 636=⋅=(b)344446455551254 is used as a factor 3 times.5⋅⎛⎞=⎜⎟⎝⎠⋅=2.(a)1062103Divide.7Subtract.−÷=−=(b)()( )182 63182 3Subtract inside parentheses.186Multiply.24Add.+−=+=+=(c)()()7 63 817 63 9Add inside parentheses.4227Multiply.15Subtract.⋅−+=⋅−=−=(d)2232295 2Apply exponents.2910Multiply.1110Add.1Subtrac5t.+⋅=+−⋅=+−=−=−N2.(a)152 61512Multiply.3Subtract.−⋅=−=(b)()()82 5182 4Subtract inside parentheses.88Multiply.16Add.+−=+=+=(c)()()6 247 56 67 5Add inside parentheses.3635Multiply.1Subtract.+−⋅=−⋅=−=(d)328 10423 48 10483 16Apply exponents.804848Multiply.20848Divide.1248Subtract.60Add.⋅÷−+⋅=⋅÷−+⋅=÷−+=−+=+=3.(a)()[][ ]9 123Add inside parentheses.9 9Subtra9483inside brct81Macketultip ys.l .=−==+−⎡⎤⎣⎦(b)2(78)23 512(15)2Add inside parentheses.3 51302Multiply.1513162Add.Divide2.=++⋅++=⋅++==+N3.(a)()[]273147[(91)4]Apply exponents.7[84]Subtract inside parentheses.7 12Add inside brackets.84Multiply.⎡⎤−+⎣⎦=−+=+==

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1.1 Exponents, Order of Operations, and Inequality27(b)9(144)243 69(10)2Subtract inside parentheses.43 6902Multiply.41888Subtract and add.224Divide.−−+⋅−=+⋅−+===4.(a)The statement 126>istruesince 12 isgreater than 6. Note that the inequalitysymbol points to the lesser number.(b)The statement 284 7≠⋅isfalsebecause 28is equal to4 7.⋅(c)The statement2121≤istruesince2121.=(d)Write the fractions with a commondenominator. The statement1134<isequivalent to the statement43 .1212<Since4 isgreaterthan 3, the original statementisfalse.N4.(a)The statement 12102≠−istruebecause12is not equal to8.(b)The statement 54 2>⋅isfalsebecause 5isless than8.(c)The statement 77≤istruesince 7.7=(d)Write the fractions with a commondenominator. The statement 57911>isequivalent to the statement 5563 .9999>Since55 islessthan 63, the original statementisfalse.5.(a)“Nine is equal to eleven minus two” iswritten as 9112.=−(b)“Fourteen is greater than twelve” is writtenas 1412.>(c)“Two is greater than or equal to two” iswritten as 22.≥N5.(a)“Ten is not equal to eight minus two” iswritten as 1082.≠−(b)“Fifty is greater than fifteen” is written as50.15>(c)“Eleven is less than or equal to twenty” iswritten as 11.20≤6.915≤may be written as 15.9≥N6.89<may be written as 9.8>Exercises1.False;233 39.=⋅=2.False; 1 raised toanypower is 1.Here,311 1 11.=⋅ ⋅=3.False; a number raised to the first power is thatnumber, so133.=4.False;26means that 6 is used as a factor 2times, so266 636.=⋅=5.False; the common error leading to 42 is adding4 to 3 and then multiplying by 6. One mustfollow the rules for order of operations.()43(82)43 641822+−=+=+=6.False; multiplications and divisions areperformedin order from left to right.122 36 318÷⋅=⋅=7.Additions and subtractions are performed inorder from left to right.NN121823−+8.Multiplications and divisions are performed inorder from left to right, and then additions andsubtractions are performed in order from leftto right.NN212862−÷9.Multiplications and divisions are performed inorder from left to right, and then additions andsubtractions are performed in order from leftto right.NNN3212 863⋅−÷

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Chapter 1 The Real Number System2810.Multiplications and divisions are performed inorder from left to right, and then additions andsubtractions are performed in order from left toright. If grouping symbols are present, workwithin them first, starting with the innermost.NNN312406( 31)+−11.Multiplications and divisions are performed inorder from left to right, and then additions andsubtractions are performed in order from left toright. If grouping symbols are present, workwithin them first, starting with the innermost.NNNN41233 52( 42)⋅−+12.Apply all exponents. Then, multiplications anddivisions are performed in order from left toright, and additions and subtractions areperformed in order from left to right.NNNN331429234−+⋅13.233 39=⋅=14.286488=⋅=15.277 749=⋅=16.241644=⋅=17.21212 12144=⋅=18.2141491146=⋅=19.344 4 464=⋅⋅=20.35 512555=⋅⋅=21.31010 10 101000=⋅⋅=22.31111 11 111331=⋅⋅=23.433 3 3 381=⋅⋅⋅=24.46 6 6 61 962 6=⋅⋅⋅=25.544 4 4 4 41024=⋅⋅⋅⋅=26.53 3 3 3 32433=⋅⋅⋅⋅=27.2111166636=⎟⋅⎞⎠=⎛⎜⎝28.211 1133 39=⎟⎠⋅⎞⎜=⎛⎝29.422222163333381=⋅⋅⋅⎛⎜=⎞⎟⎝⎠30.3344334342674=⋅⋅⎟⎠=⎛⎞⎜⎝31.()()()()30.40.40.40.40.064==32.()()() ()()40.50.50.50.0.062550.5==33.Divide.644 216 232Multiply.÷⋅=⋅=34.Divide.2505 250 2100Multiply.÷⋅=⋅=35.139 51345Multiply.58Add.+⋅=+=36.117 61142Multiply.53Add.+⋅=+=37.25.212.64.225.23Divide.22.2Subtract.=−÷=−38.12.49.33.112.43D9.ivide.Subtract4.−÷=−=39.122 1112243536155443030304919, or 13Multiply.LC03d.0DAd⋅+⋅=+===+40.245344353986175, or 29Multiply.23LCD66Add.66⋅+⋅===++=41.9 48 33624Multiply.12Subtract.=⋅−⋅=−42.11 410 34430Multipl7y.Add.4=⋅+⋅=+43.204 3520125Multiply.85Subtract.13Add.−⋅+=−+=+=

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1.1 Exponents, Order of Operations, and Inequality2944.187 2618146Multiply.46Subtract.10Add.−⋅+=−+=+=45.10405 2108 2Divide.1016Multiply.26Add.+÷⋅==+=⋅+46.1264841284Divide.204Add.16Subtract.+÷−=+−=−=47.182(34)182(7)Add inside parentheses.1814Multiply.4Subtract.−=+=−−=48.()()303 42303 6Add inside parentheses.18Multiply.12Subtrac0.3t−+=−−==49.3(42)8 33 68 3Add.1824Multiply.42Add.=++⋅=⋅++=⋅50.()Add.79 1210Multiply.8272 59 82Ad .5d=++=+⋅=⋅+⋅51.2184318163Apply exponents.23Subtract.5Add.−+=−+=+=52.322292289Apply exponents.149Subtract.23Add.−+=−+=+=53.23[54(2)]23[58]Multiply.23[13]Add.239Multiply.41Add.++=++=+=+=54.( )[][]54 17 354 121Multiply.54 22Add.588Multiply.93Add.++=++⎡⎤⎣⎦=+=+=55.()25 34 25[34(4)]Apply exponents.5(316)Multiply.5(19)Add.95Multiply.⎡⎤+=+⎣⎦=+==56.()[]36 28 36 28 27Apply exponents.6(2216)Multiply.6 218Add.1308Multiply.⎡⎤+⎣⎦=+⋅=+=⋅=57.2223 [(113)4]3 [144]Add inside parentheses.3 [10]Subtract.9[10]Apply exponents.90Multiply.+−=−===58.[][ ][ ]22249[(134)8]4178Add inside parentheses.4Subtract.16 9Apply exponents.144Multiply.+−=−===59.Simplify the numerator and denominatorseparately, and then divide.()226 3186(91)884826(8)84488456144−+−+=−−+=+===60.Simplify the numerator and denominatorseparately, and then divide.()()()232482 644829272932 6081208826212248−+−+=−−+=+===

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Chapter 1 The Real Number System3061.Simplify the numerator and denominatorseparately, and then divide.224(62)8(83)4(8)8(5)6(42)26(2)24(8)8(5)6(2)432401247298++−+=−−−+=−+=−==62.Simplify the numerator and denominatorseparately, and then divide.336(51)9(11)6(6)9(2)5(86)25(2)236181081829+−+−=−−−−=−==63.3 64 260⋅+⋅=Listed below are some possibilities. Use trialand error until you get the desired result.(3 6)4 21882660(3 64) 222 244603 (64 2)3 1442603 (64) 23 10 230 260⋅+⋅=+=≠⋅+⋅=⋅=≠⋅+⋅=⋅=≠⋅+⋅=⋅⋅=⋅=64.2 81 342⋅−⋅=()28132 7 314 342⋅−⋅=⋅⋅=⋅=65.10736−−=10(73)1046−−=−=66.151027−−=15(102)1587−−=−=67.282100+=()22821010 10100+==⋅=68.24236+=()224266 636+==⋅=69.9 311162711161616⋅−≤−≤≤The statement is true since 1616.=70.6 512183012181818⋅−≤−≤≤The statement is true since 1818.=71.5 112 360556606160⋅+⋅≤+≤≤The statement is false since 61is greaterthan60.72.9 34 5482720484748⋅+⋅≥+≥≥The statement is false since 47is less than48.73.012 36 60363600≥⋅−⋅≥−≥The statement is true since 00.=74.1013 215 11026151011≤⋅−⋅≤−≤The statement is true since 1011.<75.452[23(25)]452[23(7)]452[221]452[23]4546≥++≥+≥+≥≥The statement is false since 45is less than46.76.553[43(41)]553[43(5)]553[415]553[19]5557≥++≥+≥+≥≥The statement is false since 55is less than57.77.[3 45(2)] 372[1210] 372[22] 3726672⋅+⋅>+⋅>⋅>>The statement is false since 66is less than72.

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1.1 Exponents, Order of Operations, and Inequality3178.2 [7 53(2)]582 [356]582[29]585858⋅⋅−≤⋅−≤≤≤The statement is true since 5858.=79.35(41)32 4135(3)38131539183923+−≥⋅++≥++≥≥≥The statement is false since 2is less than3.80.()()7 312235 27 4223102822132621322+−≤+⋅−≤+−≤≤≤The statement is true since 22.=81.2(51)3(11)35(86)4 22(6)3(2)35(2)8126310863233+−+≥−−⋅−≥−−≥−≥≥The statement is true since 33.=82.()3(83)2(41)79(62)11 523(5)2(3)79(4)11(3)15673633217377−+−≤−−−+≤−+≤−≤≤The statement is true since 77.=83.“5”17<means “five is less than seventeen.”The statement is true.84.“8”12<means “eight is less than twelve.” Thestatement is true.85.“5”8≠means “five is not equal to eight.” Thestatement is true.86.“6”9≠means “six is not equal to nine.” Thestatement is true.87.“7”14≥means “seven is greater than or equalto fourteen.” The statement is false.88.“6”12≥means “six is greater than or equal totwelve.” The statement is false.89.“15”15≤means “fifteen is less than or equalto fifteen.” The statement is true.90.“21”21≤means “twenty-one is less than orequal to twenty-one.” The statement is true.91.“13”310=means “one-third is equal to three-tenths.” The statement is false.92.“106”32=means “ten-sixths is equal to three-halves.” The statement is false.93.2.52“”.50>means “two and five-tenths isgreater than two and fifty-hundredths.” Thestatement is false.94.1.80“”1.8>means “one and eighty-hundredthsis greater than one and eight-tenths.” Thestatement is false.95.“Fifteen is equal to five plus ten” is writtenas 15510.=+96.“Twelve is equal to twenty minus eight” iswritten as 12208.=−97.“Nine is greater than five minus four” is writtenas 954.>−98.“Ten is greater than six plus one” is writtenas 1061.>+99.“Sixteen is not equal to nineteen” is writtenas 1619.≠100.“Three is not equal to four” is written as 34.≠101.“One-half is less than or equal to two-fourths”is written as 12 .24≤

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Chapter 1 The Real Number System32102.“One-third is less than or equal to three-ninths”is written as 13 .39≤103.520<becomes 205>when the inequalitysymbol is reversed.104.309>becomes 930<when the inequalitysymbol is reversed.105.4354>becomes 3445<when the inequalitysymbol is reversed.106.5342<becomes 3524>when the inequalitysymbol is reversed.107.2.51.3≥becomes 1.32.5≤when theinequality symbol is reversed.108.4.15.3≤becomes 5.34.1≥when theinequality symbol is reversed.109.(a)Substitute “40” for “age” in the expressionfor women.14.740 0.13−⋅(b)14.740 0.1314.75.2Multiply9..Subtract5.=−⋅=−(c)85% of 9.5 is 0.85(9.5)8.075.=Walking at 5 mph is associated with8.0 METs,which is the table value closestto 8.075.(d)Substitute “55” for “age” in the expressionfor men.14.755 0.11−⋅14.755 0.1114.76.05M8ultiply.Subtract..65−⋅=−=85% of 8.65 is 0.85(8.65)7.3525.=Swimming is associated with 7.0 METs,which is the table value closest to 7.3525.110.Answers will vary.111.The states that had a number greater than 13.8are Alaska()16.2 , Texas()14.7 , California()24.1 , and Idaho()17.6 .112.The states that had a number that was at most14.7 are Texas()14.7 , Wyoming()12.5 ,Maine()12.3 , and Missouri()13.8 .113.The states that had a numbernotless than 13.8,which is the same as greater than or equal to13.8, are Alaska()16.2 , Texas()14.7 ,California()24.1 , Idaho()17.6 , andMissouri()13.8 .114.The states that had a number less than 13.0 areWyoming()12.5and Maine()12.3 .1.2 Variables, Expressions, and EquationsClassroom Examples, Now Try Exercises1.(a)16 3Repla1cewith 3.48Multiply.616ppp⋅=⋅==(b)333222 3Replacewith 3.2 27Cube 3.54Multiply.ppp=⋅=⋅=⋅=N1.(a)99 6Replacewith 6.54Multipl9y.xxx=⋅=⋅=(b)2224Replacewith 6.4 6Square 6.4 36Multiply.1444xxx=⋅=⋅=⋅=2.(a)454(6)5(9)2445Multipl69Add.y.xy+=++==(b)424(6)2(9)1612418Multiply.61Sub6tract add7nd axyx.=+−+=−−=+(c)2222263681Use exponents.Multiply.153A292781d .2dxy+=+==+=⋅⋅+

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1.2 Variables, Expressions, and Equations33N2.(a)343(4)4(7)1228Multipl40Add.y.xy+=++==(b)626(4)2(7)292(7)92414Multiply.149102Subtract; reduce.5xyy−−=−−−−===(c)222244 474 1649Use exponents.6449Multiply.15Subtract.xy====−⋅−⋅−−3.(a)Since a number is subtractedfrom48, writethis as 48x−when usingxas the variableto represent the number.(b)“Product” indicates multiplication. Usingxas the variable to represent the number, “theproduct of 6 and a number” translates as6x⋅or 6x.(c)“The sum of a number and 5” suggests anumber plus 5. Usingxas the variable torepresent the number, “9 multiplied by thesum of a number and 5” translates as()95 .x+N3.(a)Usingxas the variable to represent thenumber, “the sum of a number and 10”translates as0,1x+or 10.x+(b)“A number divided by 7” translates as7,x÷or.7x(c)“The difference between 9 and a number”translates as 9.x−Thus, “the product of 3and the difference between 9 and a number”translates as 3(9.)x−4.??81158 211Replacewith 2.1611M5555Trueultiply.pp−=⋅−=−==The number 2 is a solution of the equation.N4.??85618 75Replacewith61617.565Multiply.6161Truekk==+=⋅+=+The number 7 is a solution of the equation.5.Usingxas the variable to represent the number,“three times a number is subtracted from 21,giving 15” translates as 21315.x−=Now tryeach number from the set {0, 2, 4, 6, 8, 10}.()?150 :213 02115Falsex−===()?152 :213 21515Truex−===()?154 :213 4915Falsex=−==Similarly,6, 8,x=or 10 result in falsestatements. Thus, 2 is the only solution.N5.Usingxas the variable to represent the number,“the sum of a number and nine is equal to thedifference between 25 and the number”translates as925.xx+=−Now try eachnumber from the set {0, 2, 4, 6, 8, 10}.?254 :491321Fals4ex−=+==?256 :691519Fals6ex−=+==?28 :891717True58x−=+==Similarly,0, 2,x=or 10 result in falsestatements. Thus, 8 is the only solution.6.(a)315x−has no equals symbol, so this is anexpression.(b)315x=has an equals symbol, so this is anequation.N6.(a)256x+=has an equals symbol, so this isan equation.(b)256x+−has no equals symbol, so this isan expression.

Solution Manual for Beginning and Intermediate Algebra, 6th Edition - Page 15 preview image

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Chapter 1 The Real Number System34Exercises1.The expression28xmeans 8.x x⋅⋅The correctchoice is B.2.If2x=and1,y=then the value ofxyis2 12.⋅=The correct choice is C.3.The sum of 15 and a numberxis represented bythe expression 15.x+The correct choice is A.4.There is no equals symbol in 67x+or 67,x−so those are expressions. 67x=and670x−=have equals symbols, so those areequations.5.322,xx x x=⋅⋅⋅while3222(2 ) .xxxx⋅⋅=Thelast expression is equal to38.x6.“7 less than a number” is an expressionindicating subtraction,7,x−while “7 is lessthan a number” is a statement relating 7 andx, 7.x<7.The exponent 2 applies only to its base, whichisx.(The expression2(5 )xwould requiremultiplying 5 by4x=first.)8.An expression cannot be solved—it indicates aseries of operations to perform. An expressionis simplified; an equation is solved.9.(a)74711x+=+=(b)76713x+=+=10.(a)3431x−=−=(b)3633x−=−=11.(a)44(4)16x==(b)44(6)24x==12.(a)()66 424x==(b)()66 636x==13.(a)2244 44 1664x=⋅=⋅=(b)2244 64 36144x=⋅=⋅=14.(a)2255 45 1680x=⋅=⋅=(b)2255 65 36180x=⋅=⋅=15.(a)1413353x++==(b)1613373x++==16.(a)2425255x−−==(b)2624555x−−==17.(a)353 4522 4125878xx−⋅−=⋅−==(b)353 6522 6185121312xx−⋅−=⋅−==

Solution Manual for Beginning and Intermediate Algebra, 6th Edition - Page 16 preview image

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1.2 Variables, Expressions, and Equations3518.(a)()()4 414133 416112155124xx−−=−===(b)()()4 614133 6241182318xx−−=−==19.(a)2233 443 16448452xx+=⋅+=⋅+=+=(b)2233 663 3661086114xx+=⋅+=⋅+=+=20.(a)()2222 4481624xx+=+=+=(b)()2222 66123648xx+=+=+=21.(a)6.4596.459 425.836x=⋅=(b)6.4596.459 638.754x=⋅=22.(a)3.2753.275 413.1x=⋅=(b)3.2753.275 619.65x=⋅=23.(a)8358(2)3(1)5163519524xy++=++=++=+=(b)8358(1)3(5)5815523528xy++=++=++=+=24.(a)4274(2)2(1)782717xy++=++=++=(b)4274(1)2(5)7410721xy++=++=++=25.(a)3(2 )3(22 1)3(22)3(4)12xy+=+⋅=+==(b)3(2 )3(12 5)3(110)3(11)33xy+=+⋅=+==26.(a)()()()2(2)2 2 212 412 510xy+=+⎡⎤⎣⎦=+==(b)( )()()2(2)2 2 152 252 714xy+=+⎡⎤⎣⎦=+==27.(a)4421246xy+=+=+=(b)4415545595xy+=+=+=28.(a)8821145yx+=+=+=(b)18855813yx+=+=+=

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