write:x=277Notethatwedidn’tusethesolutionsetnotationhere. Forsinglesolutionswewillrarelydothatinthisclass. However ifwehadwantedtothesolutionsetnotationforthisproblemwouldbe 277Befor

x=277Notethatwedidn’tusethesolutionsetnotationhere.Forsinglesolutionswewillrarelydothatinthisclass.However
ifwehadwantedtothesolutionsetnotationforthisproblemwouldbe
277Beforeproceedingtothenextproblemlet’sfirstmakeaquickcommentaboutthe“messiness’ofthisanswer.DoNOTexpectallanswerstobenicesimpleintegers.Whilewedotrytokeepmostanswersimpleoftentheywon’tbesodoNOTgetsolockedintotheideathatananswermustbeasimpleintegerthatyouimmediatelyassumethatyou’vemadeamistakebecauseofthe“messiness”oftheanswer.(b)m23+1=2m7Okay
withthisonewewon’tbeputtingquiteasmuchexplanationintotheproblem.InthiscasewehavefractionssotomakeourlifeeasierwewillmultiplybothsidesbytheLCD
whichis21inthiscase.Afterdoingthattheproblemwillbeverysimilartothepreviousproblem.Noteaswellthatthedenominatorsareonlynumbersandsowewon’tneedtoworryaboutdivisionbyzeroissues.Let’sfirstmultiplybothsidesbytheLCD.21m23+1=2m72121m23+21(1)=2m7217(m2)+21=(2m)(3)Becarefultocorrectlydistributethe21throughtheparenthesisontheleftside.Ev-erythinginsidetheparenthesisneedstobemultipliedbythe21beforewesimplify.At©PaulDawkinsAlgebra–74–