Method of Solving a Linear Equation in One Variable

In previous topics of this unit we have learnt many basic concepts about linear equation in one variable. We know that a linear equation is that which when ... MethodofSolvingaLinearEquationinOneVariable Inprevioustopicsofthisunitwehavelearntmanybasicconceptsaboutlinearequationinonevariable.Weknowthatalinearequationisthatwhichwhenplottedonagraphsheetgivesastraightline.Alinearequationinonevariableisaequationinwhichonlyoneunknownquantityispresentintheequation.Nowinthistopicwewilllearnaboutsolvingthelinearequationinonevariable.Followingstepsmustbefollowedwhilesolvingalinearequationinonevariable:StepI:Observethelinearequationcarefully.StepII:Carefullynotethequantityyouneedtofindout.StepIII:Dividetheequationintwoparts,i.e.,L.H.S.andR.H.S.StepIV:Figureoutthetermscontainingconstantsandvariables.StepV:TransferalltheconstantsontheRightHandSide(R.H.S)oftheequationandvariablesontheLeftHandSide(L.H.S.)oftheequation.StepVI:Performthealgebraicoperationsonbothsidesoftheequationtogetthevalueofthevariable. Belowaregivenfewexamplesbasedontheaboveconcept.1.Solve:2x–4=48.Solution:Thegivenequationalinearequationinonevariablewithvariableas‘x’.So,weneedtofindoutthevalueof‘x’.           2x–4=48           2x=48+4           2x=52            x=52/2            x=26.Hence,thevalueofvariable‘x’is26.2.Solve:3x+34=13–2x.Solution: Bothsidesofthegivenequationcontainunknownquantities.So,letustransferalltheunknownquantitiesattheL.H.S.andknownquantitiesonR.H.S.So,theequationbecomes:           3x+2x=13–34            5x=-17            x=-17/5Hence,thevalueofvariable‘x’is-17/5.So,allthesimilarproblemscanbesolvedusingaboveconcepts.Nowthereareanothertypeofproblemsinlinearequationinonevariable.Thesearewordproblemsonlinearequationsinonevariable.Linearequationinonevariablecanbesolvedusingfollowingsteps:StepI:Firstofallreadthegivenproblemcarefullyandnotedownthegivenandrequiredquantitiesseparately.StepII:Denotetheunknownquantitiesas‘x’,‘y’,‘z’,etc. StepIII:Thentranslatetheproblemintomathematicallanguageorstatement.StepIV:Formthelinearequationinonevariableusingthegivenconditionsintheproblem.StepV:Solvetheequationfortheunknownquantity. Nowletussolvesomeproblemsbasedonaboveconcepts:1. Thesumoftwonumbersis36.Thenumbersaresuchthatoneofthemis5timestheothernumber.Findthenumbers.Solution:Letoneofthenumbersbe‘x’. Then,2ndnumber=5x.Itisgiventhattheirsumis36.So,x+5x=36.6x=36.x=36/6.x=6.Hence1stnumber=6.2ndnumber=5x=5x6=30.2. Afatheris4timesolderthanhisson.Ifsumofagesofbothfatherandsonis50years.Thenfindtheageofbothofthem.Solution:Lettheageofsonbe‘x’years.Then,father’sage=4xyears.Itisgiventhatsumoftheiragesis50years.So,x+4x=505x=50x=10.So,son’sage=10years.Father’sage=4x=40years. 9thGradeMathFromMethodofSolvingaLinearEquationinOneVariabletoHOMEPAGE New!CommentsHaveyoursayaboutwhatyoujustread!Leavemeacommentintheboxbelow.AskaQuestionorAnsweraQuestion. Didn'tfindwhatyouwerelookingfor?Orwanttoknowmoreinformation aboutMathOnlyMath. UsethisGoogleSearchtofindwhatyouneed. Sharethispage: What’sthis? FacebookTwitterPinterestWhatsAppMessenger HomeMathBlogPreschoolActivitiesKindergartenMath1stGradeMath2ndGradeMath3rdGradeMath4thGradeMath5thGradeMath6thGradeMath7thGradeMath8thGradeMath9thGradeMath10thGradeMath11&12GradeMathAlgebra1ConceptsofSetsMatrixProbabilityStatisticsLogarithmsBooleanAlgebraMathColoringPagesMultiplicationTableCoolMathsGamesMathFlashCardsOnlineMathQuizMathPuzzlesBinarySystemMathDictionaryConversionChartHomeworkSheetsMathProblemAnsFreeMathAnswersPrintableMathSheetFunnyMathAnswersEmploymentTestMathPatternsLinkPartnersAboutUsContactUsSiteMap [?]SubscribeToThisSite E-mailAddress FirstName Then Don'tworry—youre-mailaddressistotallysecure. IpromisetouseitonlytosendyouMathOnlyMath. ©and™math-only-math.com.AllRightsReserved.2010-2022.