3,000 Solved Problems in Calculus 11 - 4 CHAPTER 1 Fig 1-8...

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4Solve(2jt+l)(jt-3)Cx+7)<0.x =3. ForA:to theleftofx--l,allthree factorsarenegativeand,therefore,AT(x)isnegative. Whenwepass fromlefttoright throughx =7,*+ 7changes sign,and,therefore,K(x)becomespositive.Whenwelaterpassthroughx = -\,2x +1changes sign,and,therefore,K(x)becomesnegative again. Finally,aswepass throughx =3,x3changes signandK(x)becomesandremainspositive.Hence,K(x)isnegative whenandonly whenx<-7or 3 < * < 7.AnswerDoesSolveA->x2.Solvex2>x\Findallsolutionsof yareboth positive,orxandyareboth negative,multiplicationby thepositive quantityjcvyieldstheequivalentinequalityy <x.Solve (x-l)(x-2)(x-3)(x-4)<0.Solve (x-l)(x-2)(x-3)(x-4)<0.points4, 3,2,1.Hence,theinequality holds when

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