Solution Manual for Algebra for College Students, 8th Edition

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INSTRUCTOR’SSOLUTIONSMANUALDANIELS.MILLERNiagara County Community CollegeALGEBRAFORCOLLEGESTUDENTSEIGHTHEDITIONRobert BlitzerMiami Dade College

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TABLE OF CONTENTS for INSTRUCTOR SOLUTIONSALGEBRA FORCOLLEGESTUDENTSChapter1:Algebra, Mathematical Models, and Problem Solving1Chapter2:Functions and Linear Functions67Chapter3:Systems of Linear Functions131Chapter4:Inequalities and Problem Solving251Chapter5:Polynomials, Polynomial Functions, and Factoring331Chapter6:Rational Expressions, Functions, and Equations423Chapter7:Radicals, Radical Functions, and Rational Exponents587Chapter8:Quadratic Equations and Functions677Chapter9:Exponential and Logarithmic Functions839Chapter 10:Conic Sections and Systems of Nonlinear Equations943Chapter 11:More on Polynomial and Rational Functions1051Chapter 12:Sequences, Induction, and Probability1135

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Chapter 1Algebra, Mathematical Models, and Problem Solving11.1 Check Points1.a.eight times a numberfive more8585xxb.the quotient of adecreased bynumber and seventwice the number2277xxxx2.replacewith 10230.12230.12(10)231.221.8xxAt age 10, the average neurotic level is 21.8.3.replacewith 1322286(3)86(133)86(10)86(100)8600608xx4.a.2010 is 10 years after 2000.replacewith 10224654117,65046(10)541(10)17,65046(100)541(10)17,6504600541017,65027,660xDxxDThe formula indicates that the mean student-loandebt for college students who graduated in 2010was $27,660.b.The model value, $27,660, is more than theactual data value, $26,682. Thus, themathematical model overestimates by $978.5.a.true; Because the number 13 is an element of theset of integers.b.true; Because 6 is not an element of{7, 8, 9, 10},the statement is true.6.a.8is less than2;trueb.7 is greater than3;truec.1is less than or equal to4;falsed.5 is greater than or equal to 5; truee.2 is greater than or equal to14;true7.a.25xxb.13.5xxc.1x x 1.1 Concept and Vocabulary Check1.variable2.expression3.bth to thenth power; base; exponent4.formula; modeling; models5.natural6.whole7.integers8.rational9.irrational10.rational; irrational11.left12.2; 5; 2; 513.greater than14.less than or equal to

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Chapter 1Algebra, Mathematical Models, and Problem Solving21.1 Exercise Set1.5x2.6x3.4x4.9x5.4x6.2x7.210x8.54x9.162x10.132x11.42x12.53x13.35x14.610x15.75(10)7505716.86 58303817.6(3)81881018.8 342442019.21111339931120.21111224421121.276(7)349423731022.287 8464564841223.3345(97)45(2)45(8)4404424.  3365 8665 265 86404625.283(82)643(6)64184626.284 83644 564204427.{1, 2, 3, 4}28.{1, 2, 3}29.{–7, –6, –5, –4}30.{–6, –5, –4, –3}31.{8, 9, 10, . . .}32.{10, 11, 12, . . .}33.{1, 3, 5, 7, 9}34.{1, 3, 5, 7}35.true; Seven is an integer.36.true; Nine is an integer.37.true; Seven is a rational number.38.true; Nine is a rational number.39.false; Seven is a rational number.40.false; Nine is not an irrational number.41.true; Three is not an irrational number.42.true; Five is not an irrational number.43.false;12is a rational number.44.false;14is a rational number.45.true;2is not a rational number.46.true;πis not a rational number.47.false;2is a real number.

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Section 1.1Algebraic Expressions, Real Numbers, and Interval Notation348.false;πis a real number.49.–6 is less than –2; true50.–7 is less than –3; true51.5 is greater than –7; true52.3 is greater than –8; true53.0 is less than –4; false. 0 is greater than –4.54.0 is less than –5; false. 0 is greater than –5.55.–4 is less than or equal to 1; true56.–5 is less than or equal to 1; true57.–2 is less than or equal to –6; false. –2 is greaterthan –6.58.–3 is less than or equal to –7; false. –3 is greaterthan –7.59.–2 is less than or equal to –2; true60.–3 is less than or equal to –3; true61.–2 is greater than or equal to –2; true62.–3 is greater than or equal to –3; true63.2 is less than or equal to12; false. 2 is greaterthan12.64.4 is less than or equal to12; false. 4 is greaterthan12.65.16xx66.24xx67.52xx68.43xx69.31xx70.25xx71.2x x72.3x x73.3x x 74.5x x 75.3x x76.2x x77.5.5x x78.3.5x x79.true80.true81.false;31, 2,3, 4.82.false;41, 2, 3, 4,5.

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Chapter 1Algebra, Mathematical Models, and Problem Solving483.true84.true85.false; The value of {x|xis an integer between3and 0} ={ 2,1}, not{ 3,2,1,0}.86.false; The value of {x|xis an integer between4and 0} ={ 3,2,1}, not{ 4,3,2,1, 0}.87.false; Twice the sum of a number and three isrepresented by23x, not23x.88.false; Three times the sum of a number and five isrepresented by35x, not35x.89.4.60.024.60.02(20)4.2RxThe average resistance to happiness at age 20 is 4.2.90.4.60.024.60.02(30)4.0RxThe average resistance to happiness at age 30 is 4.0.91.[4.60.02(30)][4.60.02(50)]4.03.60.4The difference between the average resistance tohappiness at age 30 and at age 50 is 0.4.92.[4.60.02(20)][4.60.02(70)]4.23.21.0The difference between the average resistance tohappiness at age 20 and at age 70 is 0.4.93.  22328.70.3328.7 40.3 43234.84.862SxxAccording to the formula, 67% of American adultsused smartphones to go online in 2013. The formulaunderestimated the actual value by 1%.94.  22328.70.3328.7 30.3 33226.12.755.4SxxAccording to the formula, 55.4% of Americanadults used smartphones to go online in 2012. Theformula overestimated the actual value by 0.4%.95.5 (5032)9C5 (18)10910°C is equivalent to 50°F.96.555(32)(8632)(54)30999CF30°C is equivalent to 86°F.97.2246016460(2)16(2)412016(4)4120641246460httTwo seconds after it was kicked, the ball’s heightwas 60 feet.98.2246016460(3)16(3)418016(9)418014418414440httThree seconds after it was kicked, the ball’s heightwas 40 feet.99. – 116.Answers will vary.117.does not make sense; Explanations will vary.Sample explanation: Many models work for a whileand then no longer are valid beyond a certain point.118.does not make sense; Explanations will vary.Sample explanation: Though this value is beyondthe capabilities of a calculator, it still exists. Thisparticular expression can be obtained via severalsoftware applications.119.makes sense120.does not make sense; Explanations will vary.Sample explanation: The model can be used toestimate the number in 2000 by letting0.x

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression5121.false; Changes to make the statement true will vary.A sample change is: Every integer is a rationalnumber.122.false; Changes to make the statement true will vary.A sample change is: Some integers are not wholenumbers.123.true124.true125.Evaluate the two expressions.2 4202 24482 42082028Since the bird lover purchases17of the birds, theexpression has to be a multiple of 7. Since 48 in nota multiple of 7 and 28 is a multiple of 7, we knowthat the correct expression is2 420.126.2 33545127.824310or824310128.26 is not a perfect square and26cannot besimplified. Consider the numbers closest to 26,both smaller and larger, which are perfect squares.The first perfect square smaller than 26 is 25. Thefirst perfect square larger than 26 is 36. We knowthat the square root of 26 will lie between thesenumbers. We have362625.  If wesimplify, we have6265.  Therefore,26lies between –6 and –5.129.–5 and 5 are both a distance of five units from zeroon a real number line.130.4163(2)163(16)164864812(106)12(4)88131.2(35)2(3(4)5)2(125)2(17)34x6106(4)10241034x1.2 Check Points1.a.66because6is 6 units from 0.b.4.54.5because 4.5 is 4.5 units from 0.c.00because 0 is 0 units from 0.2.a.10( 18)28  b.0.20.90.7c.3165152101010  3.a.If8,x then( 8)8.x  b.If13,xthen13.x 4.a.7107( 10)3  b.4.3( 6.2)4.36.210.5 c.4141355555  5.a.2( 5)( 5)( 5)25b.25(5 5)25  c.3( 4)( 4)( 4)( 4)64 d.4333338155555625         6.a.3284 b.25248343515 7.2235122( 4)325122(16)3256(16)32596229674 

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Chapter 1Algebra, Mathematical Models, and Problem Solving68.343( 2)2(69)43( 8)2( 3)424232054  9.Commutative Property of Addition:4994xxCommutative Property of Multiplication:4949xx10.a.6(12)(612)18xxxb.7(4 )( 7 4)28xxx 11.4(72)288xx 12.22222231411(14)(311 )(141)(311)1514xxxxxxxxxxxx13.8(25)416404164401240xxxxxxx14.64[7(2)]64[72]64[9]6364424xxxxx1.2 Concept and Vocabulary Check1.negative number2.03.positive number4.positive number5.positive number6.negative number7.positive number8.divide9.subtract10.absolute value; 0;a11.a;a12.0; inverse; 0; identity13.ba14.()ab c15.abac16.simplified1.2 Exercise Set1.772.10103.444.13135.7.67.66.8.38.37.22ππ8.33ππ9.2210.3311.2255  12.771010  

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression713.3( 8)11  14.5( 10)15  15.14104 16.1569 17.6.82.34.5 18.7.92.45.5 19.113119215515151520.747421051052781101010    21.2323949482735363636   22.34345757212041353535   23.3.7( 4.5)8.2  24.6.2( 5.9)12.1  25.0( 12.4)12.4  26.0( 15.3)15.3  27.12.4( 12.4)0 28.15.3( 15.3)0 29.1111xx 30.1313xx 31.55xx 32.99xx 33.00xx34.22xx 35.31531512  36.42042016  37.8( 10)81018 38.7( 13)71320 39.20( 5)20515   40.30( 10)301020   41.11111214242444 42.12121221051051052143101010    43.2.3( 7.8)2.37.85.5  44.4.3( 8.7)4.38.74.4  45.02022 46.03033 47.9( 10)90 48.8( 10)80 49.3113350.7117751.151511313 

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Chapter 1Algebra, Mathematical Models, and Problem Solving852.111111313 53.20054.3 0055.421818 56.53215230 57.2( 3)( 1)( 2)( 4)( 6)( 1)( 2)( 4)(6)( 2)( 4)( 12)( 4)4858.32153615365330390  59.210101010060.28886461.2101010100  62.288864  63.322228 64.3333327 65.411111166.44444425667.Since a product with an odd number of negativefactors is negative,3311. 68.A product with an odd number of negative factors isnegative.3511 69.31111122228       70.311111444464       71.1234 72.3065 73.9045274.5511575.004.676.005.377.4.60is undefined.78.5.30is undefined.79.17199292714 80.1315525236 81.265306155122  82.289728369122  83.4( 5)6( 3)20( 18)20182    84.8( 3)5( 6)24( 30)24306   85.223( 2)4( 3)3(4)4(9)123624 86.225( 3)2( 2)5(9)2(4)45837

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression987.2281624364164 43644 43641634834588.221010052310010025 231004 23100839238989.2222225 235 299( 2)3( 2)109921111121  90. 2221023 453 45121736123 2126691.832(25)4(86)832( 3)4(2)83 68832861492.832(57)5(42)832( 2)5(2)83 41083 41083681826 93.22434128858333 94.64532415999101195. 222562 37124893 25893 512 48975187114142 96.222123 5 23123 5 497336736123 5 131036123 5(13)4 5(13)262620(13)260102626 97.153( 1)122 3154122 3152122 31526 315218131831 98.1752122 3177122 3177122 31776 317718101828 99.2222201105122011062201100362201642201822011637100. 2222435213243(3)1324922434842  101.Commutative Property of Addition410104xxCommutative Property of Multiplication410410xx102.Commutative Property of Addition530305xxCommutative Property of Multiplication530530xx103.Commutative Property of Addition7557xx Commutative Property of Multiplication7575xx

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Chapter 1Algebra, Mathematical Models, and Problem Solving10104.Commutative Property of Addition3773xx Commutative Property of Multiplication3737xx105.4(6)(46)10xxx106.12(3)(123)15xxx107.7(3 )( 7 3)21xxx 108.10(5 )( 10 5)50xxx 109.11( 3 )333yyy 110.11( 4)444yyy 111.3(25)3 23 5615xxx112.5(47)5 45 72035xxx113.7(23)7 27 31421xxx   114.9(32)9 39 22718xxx   115.(36)1 31 636xxx    116.(63)1 61 363xxx   117.757512xxxx118.81081018xxxx119.22226615xxxx120.22229918xxxx121.2222226104264102641021012xxxxxxxxxxxx122.222295349354129xxxxxxxx123.8(35)68 38 562440624640246401840xxxxxxxxxx124.7(45)87 47 5828358288352035xxxxxxxx125.5(32)725 35 21 71 215107215710215712812yyyyyyyyyy 126.4(53)634 54 (3)1 61 3201263206151415yyyyyyyy 127.74 34574 34571216201625yyyy128.65 82465 82465 12265 1252660101054yyyyyy 129.2222222222221846251846125184671846718647186111211xxxxxxxxxxxx

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Section 1.2Operations with Real Numbers and Simplifying Algebraic Expression11130.2222221457241457144145710xxxxxx22222214571014751014715715xxxxxx131.444xxxx 132.8828xxxxx133.6530xx 134.10440xx 135.523xxx136.62628xxxxx 137.83683656xxxxx138.8368318310xxx 139.21( 29)8  140.4( 10)6  141.21( 29)212950 142.4( 10)41014 143.3( 10)3107  The approval rating of France exceeds the approvalrating of China by 7.144.3( 29)32926  The approval rating of France exceeds the approvalrating of Iran by 26.145.10( 3)49333  The average approval rating of China, France, andIsrael is3.146.29( 10)2118336  The average approval rating of Iran, China, and theUK is6.147. 221.21.6(40)1.2 61.6(640)116.8DxxAccording to the model, college students spent$116.8 billion in 2013.The model underestimates the actual valuedisplayed in the graph by $0.2 billion.148. 221.21.6(40)1.2 41.6(440)89.6DxxAccording to the model, college students spent$89.6 billion in 2011.The model overestimates the actual value displayedin the graph by $2.6 billion.149.a.0.050.12 10,0000.0512000.1212000.07xxxxxb.0.05 60000.12 10,00060000.05 60000.12 400030048078012000.07 60001200420780The total interest will be $780.150.a.0.060.5(50)0.06250.5250.44tttttb.0.06(20)0.5(5020)0.06(20)0.5(30)1.21516.2250.44(20)258.816.2The total distance will be 16.2 miles.

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Chapter 1Algebra, Mathematical Models, and Problem Solving12151. – 167.Answers will vary.168.makes sense169.makes sense170.does not make sense; Explanations will vary.Sample explanation: For terms to be considered liketerms they must have the same variables and thesame powers.171.does not make sense; Explanations will vary.Sample explanation: When there is no number infront of a variable, the coefficient has a value of 1.172.false; Changes to make the statement true will vary.A sample change is:164 24 28173.false; Changes to make the statement true will vary.A sample change is:62 4362 76148 174.false; Changes to make the statement true will vary.A sample change is:53(4)531237xxx175.false; Changes to make the statement true will vary.A sample change is:2xxx 176.true177.(82) 3414178.12 5109452179.229 4(16)(39)9 47( 6)1212556655213 9336125522736125363546397 180.104xx181.444102(5)102(75)102(2)102 16103242x182.true;12is not an irrational number.183.x24yx−324( 3)495y  −224( 2)440y −124( 1)413y 024(0)404y124(1)413y224(2)440y324(3)495y 184.x21yx−321( 3)198y  −221( 2)143y  −121( 1)110y 021(0)101y121(1)110y221(2)143y 321(3)198y 185.x1yx−44133y  −33122y  −22111y  −11100y 00111y11122y22133y

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Section 1.3Graphing Equations131.3 Check Points1.2.Make a table:222222221( ,)31( 3)8( 3,8)21( 2)3( 2,3)11( 1)0( 1, 0)01(0)1(0,1)11(1)0(1, 0)21(2)3(2,3)31(3)8(3,8)xyxx yyyyyyyy=−−=− −= −−−−=− −= −−−−=− −=−=−==−==−= −−=−= −−3.Make a table:1( ,)44133( 4,3)33122( 3, 2)22111( 2,1)11100( 1,0)00111(0,1)11122(1, 2)22133(2,3)xyxx yyyyyyyy       4.a.The drug concentration is increasing from 0 to 3hours.b.The drug concentration is decreasing from 3 to13 hours.c.The drug’s maximum concentration is 0.05milligram per 100 milliliters, which occurs after3 hours.d.None of the drug is left in the body.5.The minimumx-value is –100, the maximumx-value is 100, and the distance between consecutivetick marks is 50. The minimumy-value is –100, themaximumy-value is 100, and the distance betweenconsecutive tick marks is 10.1.3 Concept and Vocabulary Check1.x-axis2.y-axis3.origin4.quadrants; four5.x-coordinate;y-coordinate6.solution; satisfies

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Chapter 1Algebra, Mathematical Models, and Problem Solving141.3 Exercise Set1. – 10.11.x,x y−33,5−22, 0−11,300,411,322,033,512.x,x y−33, 0−22,5−11,800,911,822,533, 013.x,x y−33,5−22,4−11,300,211,122,033,1

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Section 1.3Graphing Equations1514.x,x y−33,1−22, 0−11,100, 211,322, 433,515.x,x y−33,5−22,3−11,100,111,322,533, 716.x,x y−33,10−22,8−11,600,411,222,033, 217.x,x y−333, 2−22,1−111, 200,0111,222,1333,2

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Chapter 1Algebra, Mathematical Models, and Problem Solving1618.x,x y−373, 2−22,3−151, 200, 2131, 222,1313, 219.x,x y−33, 4−22,3−11, 200,111, 222,333, 420.x,x y−33, 2−22,1−11, 000,111,022,133, 221.x,x y−33, 6−22, 4−11, 200,011, 222, 433, 6

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Section 1.3Graphing Equations1722.x,x y−33,6−22,4−11,200,011,222,433,623.( ,)3( 3,9)2( 2,4)1( 1,1)0(0,0)1(1,1)2(2,4)3(3,9)xx y24.( ,)93( 3,)22( 2,2)11( 1,)20(0,0)11(1,)22(2,2)93(3,)2xx y25.( ,)3( 3,27)2( 2,8)1( 1,1)0(0,0)1(1,1)2(2,8)3(3, 27)xx y

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Chapter 1Algebra, Mathematical Models, and Problem Solving1826.x,x y−33,28−22,9−11,200,111,022,733, 2627.[–5, 5, 1] by [–5, 5, 1]This matches graph c.28.[–10, 10, 2] by [– 4, 4, 2]This matches graph d.29.[–20, 80, 10] by [–30, 70, 10]This matches graph b.30.[–40, 40, 20] by [–1000, 1000, 100]This matches graph a.31.The equation that corresponds to2Yin the table is(c),22yx. We can tell because all of thepoints( 3,5),( 2, 4),( 1,3),(0, 2),(1,1),(2,0), and(3,1)are on the line2yx, but allare not on any of the others.32.The equation that corresponds to1Yin the table is(b),21yx. We can tell because all of the points( 3,9),( 2, 4),( 1,1),(0,0),(1,1),(2, 4), and(3,9)are on the graph2yx, but all are not onany of the others.33.No. It passes through the point(0, 2).34.Yes. It passes through the point(0,0).35.(2,0)36.(0, 2)37.The graphs of1Yand2Yintersect at the points( 2, 4)and(1,1).38.The values of1Yand2Yare the same when2x and1x.39.24yx40.42yx

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Section 1.3Graphing Equations1941.23yx42.22yx43.( ,)3( 3,5)2( 2,5)1( 1,5)0(0,5)1(1,5)2(2,5)3(3,5)xx y44.( ,)3( 3,1)2( 2,1)1( 1,1)0(0,1)1(1,1)2(2,1)3(3,1)xx y45.( ,)122,211,111 ,22211 ,33311 ,33311 , 22211,1122, 2xx y

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Chapter 1Algebra, Mathematical Models, and Problem Solving2046.( ,)122, 211,111 , 22211 ,33311 ,33311 ,22211,1122,2xx y47.The greatest percentage of the U.S. population thatused the internet was 84%, in 2013.48.The least percentage of the U.S. population thatused the internet was 70%, in 2011.49.The percentage of the U.S. population that used theinternet remained constant in 2009 and 2010 at71%.50.The percentage of the U.S. population that used theinternet increased most rapidly between 2011 and2012. It increased by 9%.51.The percentage of the U.S. population that used theinternet decreased most rapidly between 2008 and2009. It decreased by 3%.52.Between 2007 to 2013, the increase was 9%.53.At age 8, women have the least number ofawakenings, averaging about 1 awakening pernight.54.At age 65, men have the greatest number ofawakenings, averaging about 8 awakenings pernight.55.The difference between thenumber of awakeningsfor 25-year-old men and women is about 1.9.56.The difference between thenumber of awakeningsfor 18-year-old men and women is about 1.1.57.graph a58.graph d59.graph b60.graph c61.graph b62.graph a63.graph c64.graph b65. – 72.Answers will vary.73.makes sense74.does not make sense; Explanations will vary.Sample explanation: Most graphing utilities do notdisplay numbers on the axes.75.makes sense

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Section 1.4Solving Linear Equations2176.does not make sense; Explanations will vary.Sample explanation: There may or may not be amathematical model that perfectly describes thegraph’s data.77.false; Changes to make the statement true will vary.A sample change is: If the product of a point’scoordinates is positive, the point could be inquadrant I or III.78.false; Changes to make the statement true will vary.A sample change is: When a point lies on thex-axis,y= 0.79.true80.false; Changes to make the statement true will vary.A sample change is: Substituting the coordinates of(2,5)into324yx gives3(5)2(2)4 which simplifies to114 which is false.81.The four hour day costs $6 and the five hour daycosts $9. Thus the total cost for the two days is $15.82.Your car was parked more than six hours, but notexceeding eight hours.83.14.314.384.1213179610124941249416133  85.65 4310620151062015101425xxxxxx 86.43564( 9)35( 9)63634563939xx  The statement is true for9.x 87.133(2)133673xxx88.311021031125(31)155xxxx1.4 Check Points1.4529455295424424446xxxxxThe solution set is {6}.Check:45294(6)529245292929x2.2126453121143114128888881xxxxxxxxxxx  The solution set is {–1}.Check:2126452( 1)12( 1)6( 1)45( 1)21216451515xxxx   

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Chapter 1Algebra, Mathematical Models, and Problem Solving223.2(3)17133(2)261713362237323723530530556xxxxxxxxxxxThe solution set is {6}.Check:2(3)17133(2)2(63)17133(62)2(3)17133(8)61713241111xx 4.5357414xx 53528287414285283285171411445732 54207211011110111011111111111111xxxxxxxxxxxxxThe solution set is {1}.Check:5357414151357414625741424141028282810102828xx5.474(1)347443474171xxxxxx This equation is an inconsistent equation and thushas no solution.The solution set is { }.6.799(1)279992797999xxxxxxxxThis equation is an identity and all real numbers aresolutions.The solution set isis a real numberx xor(,) or.7.394312311, 397394312311,39731233948274394827439439439421TxxxxxxThe average cost of tuition and fees at publiccolleges will reach $11,397 in the school yearending 21 years after 2000, or 2021.1.4 Concept and Vocabulary Check1.linear2.equivalent3.bc4.bc5.apply the distributive property6.least common denominator; 127.inconsistent;8.identity;(,) 1.4 Exercise Set1.5318533183515515553xxxxxThe solution set is {3}.

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Section 1.4Solving Linear Equations232.385034214xxxThe solution set is {14}.3.63636336336666666611xxxxxThe solution set is {11}.4.587258016xxxThe solution set is {16}.5.145411451441145555555511xxxxx   The solution set is {11}.6.25683610818xxx  The solution set is {18}.7.11654011654055405554055357xxxxxxxxThe solution set is {7}.8.528355283538353279xxxxxxxThe solution set is {9}.9.276276xxxxxx76x776713xxThe solution set is {13}.10.352135138xxxxThe solution set is {8}.11.741674166416644164612612662xxxxxxxxxxxThe solution set is {2}.12.742814371436xxxxxThe solution set is {6}.13.83119883118933939399123123334yyyyyyyyyyyThe solution set is {–4}.14.5292242441yyyyyThe solution set is {–1}.15.32725367210xxxx326722106710110111019xxxxxxxxThe solution set is {9}.

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Chapter 1Algebra, Mathematical Models, and Problem Solving2416.21331223332123413441xxxxxxxxxxx    The solution set is {–1}.17.3443323124123255xxxxxxxxxx The solution set is {–5}.18.2751332751337313343134164xxxxxxxxx The solution set is {–4}.19.16317163371624164244122122226xxxxxxxxxThe solution set is {6}.20.52235522353245253xxxxxxxxxxxxThe solution set is {3}.21.71437743774 23778127778712712712121219xxxxxxxxxxxxxxxxxThe solution set is {19}.22.2 346562 34653026530212530127304276xxxxxxxxxxxxxThe solution set is {6}.23.1248169122324166821268812882020582zzzzzzzzz   The solution set is52.24.3224816694318616462646226242zzzzzzzzz    The solution set is {–2}.25.2326623223122333121212xxxxxxxxxxxx The solution set is {12}.26.1563030156xxxx653030xxxThe solution set is {30}.

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Section 1.4Solving Linear Equations2527.2032620632120231202232120512055524xxxxxxxxxxxxxThe solution set is {24}.28.152613030526615515015xxxxxxxxThe solution set is {15}.29.32153321515153910159101010151515xxxxxxxxxxxx The solution set is {–15}.30.352434452423202020xxxxxxxx The solution set is {–20}.31.3551023510105102xxxxxx610254254255255xxxxxxxxxxx The solution set is {5}.32.217272221714214722282 277 172847119247119171197xxxxxxxxxxxxxxxxThe solution set is {7}.33. 325634325121212634234 2352683152637671313xxxxxxxxxxxxx  The solution set is {13}.34.11246311212124633124 233284331047310xxxxxxxxxxx771xxThe solution set is {1}.35.3243312122433244332441231243412441212xxxxxxxxxxxxxxxx The solution set is {–12}.

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Chapter 1Algebra, Mathematical Models, and Problem Solving2636.23538xx2324 524381208233120816391048391045959519xxxxxxxxxxx  The solution set is {–19}.37.12537xx122121 537711053277105367371053361079910929246105xxxxxxxxxxxxxThe solution set is465.38.332523xxx33230305236 31531021815451020345102045720257257xxxxxxxxxxxxxxThe solution set is257.39.59914599945959xxxxxxxxThe solution set isis a real numberx xor(,) or. The equation is an identity.40.47713477734747xxxxxxxxThe solution set isis a real numberx xor(,) or. The equation is an identity.41.3273367333673367yyyyyyyyThere is no solution. The solution set isor.The equation is inconsistent.42.452144202142021yyyyThere is no solution. The solution set isor.The equation is inconsistent.43.103831083883200xxxxxxxxThe solution set is0 .The equation isconditional.44.5727377300xxxxxThe solution set is0 .The equation isconditional.45.1 620824231082832282810zzzzzzzz  The solution set is10 .The equation isconditional.

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Section 1.4Solving Linear Equations2746.116122030835244682442263zzzzzzzz The solution set is3 .The equation isconditional.47.43 227246672267267xxxxxxxxThere is no solution. The solution set isor.The equation is inconsistent.48.33 261363666666xxxxxxxxThe solution set isis a real numberx xor(,) or. The equation is an identity.49.3 42615126665136116yyyyyyyyyy266200yyyThe solution set is {0}. The equation is conditional.50.93 652 399181561824185182918182900yyyyyyyyyyyyy  The solution set is0 .The equation isconditional.51.3(4)3(22 )2xxx52.3(25)5217xxx53.3(3)5(2)0.5xxx54.254(31)20.7xxx 55.Solve:4(2)242(2)4824424664264221xxxxxxxxxxx  Now, evaluate2xxfor1x :22( 1)( 1)1( 1)112xx  56.Solve:2(6)32(21)2123422127251225102xxxxxxxxxxx  Now, evaluate2xxfor2x :22( 2)( 2)4( 2)426xx  57.Solve forx:3(3)2653(3)5(26)39103079307213xxxxxxxxx Solve fory:210518710187284yyyyy Now, evaluate2()xxyyfor3x and4y :222()( 3)3( 4)( 4)( 3)12( 4)9(124)9167xxyy    

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Chapter 1Algebra, Mathematical Models, and Problem Solving2858.Solve forx:1365241364(52)1362087687142xxxxxxxxx Solve fory:57(4)157281572958298243yyyyyyyyy Now, evaluate2()xxyyfor2x and3y :222()( 2)2( 3)( 3)( 2)6( 3)4(63)495xxyy    59.223634549345481345427 454108542xxxxxx     The solution set is2.60. 33324 53884 2884 8883282483xxxxxx     The solution set is3.61.35128763 2555128763 212555128763 1275512872 1275512872545512872545512122465246xxxxxxxxxxxxxxxxxxxx  The final statement is a contradiction, so theequation has no solution. The solution set is.62.2 558104 213.51110116104 61110116104510116102011620xxxxxxxx The final statement is a contradiction, so theequation has no solution. The solution set is.63.0.70.4(20)0.5(20)0.780.5100.28100.2210xxxxxxxThe solution set is {10}.64.0.5(2)0.13(0.10.3)0.510.10.30.90.510.310.2110.200xxxxxxxxxThe solution set is {0}.

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