Question

Resolva em R| a inequação-quociente (x-1)(2-x)(-x+4)<0. Ajudem Por Favor !!!!!?

Answer 1

Resolver a inequação

$\mathtt{(x-1)(2-x)(-x+4)\ \textless \ 0}$


Primeiro termo

x -1<0

x<1


Segundo termo

2 - x<0

x>2


Terceiro termo

-x+4<0

x>4


Fazendo o diagrama de sinais

$\begin{array}{cc} \mathtt{x\ \textless \ 1}\qquad \qquad \qquad \qquad~&~\mathtt{\underline{--}\underset{1}{\circ}\underline{+++++++++++++}} \end{array}\\\\\\ \begin{array}{cc} \mathtt{x\ \textgreater \ 2}\qquad \qquad \qquad \qquad~&~\mathtt{\underline{-----}\underset{2}{\circ}\underline{++++++++++}} \end{array}\\\\\\ \begin{array}{cc} \mathtt{x\ \textgreater \ 4}\qquad \qquad \qquad \qquad~&~\mathtt{\underline{--------}\underset{4}{\circ}\underline{+++++++}} \end{array}$

$\begin{array}{cc} \mathtt{(x\ \textless \ 1)(x\ \textgreater \ 2)(x\ \textgreater \ 4)}~&~\mathtt{\underline{--}\underset{1}{\circ}\underline{+++}\underset{2}{\circ}\underline{--}\underline{-}\underset{4}{\circ}\underline{+++++++}} \end{array}$


Conjunto solução:  $\mathtt{S=]-\infty ,1[ ~\cup~]2,4[}$


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