Question

resolva a inequaçao produto e quociente: A) x-1/3x+4 ≤0 (alguem sabe por favor preciso urgente!)

Answer 1

Resolver a inequação

$\mathtt{\dfrac{x-1}{3x+4}\leq 4}\quad\quad\texttt{com }\mathtt{x\ne -\dfrac{4}{3}}$


Para o numerador

$\mathtt{x-1 \leq 0}\\\\ \mathtt{x \leq 1}$


Para o denominador

$\mathtt{3x+4 \leq 0}\\\\ \mathtt{3x \leq -4}\\\\ \mathtt{x \leq - \dfrac{4}{3} }$


Analisando os sinais

$\begin{array}{cc} \mathtt{N}~&~\mathtt{\underline{---------}\underset{1}\bullet \underline{+++}} \end{array}\\\\ \begin{array}{cc} \mathtt{D}~&~\mathtt{\underline{---}\underset{-4/3}{\circ}\underline{++++++++}} \end{array}\\\\\\ \begin{array}{cc} \mathtt{Q}~&~\mathtt{\underline{+++}\underset{-4/3}{\circ} \underline{----}\underset{1}\bullet \underline{+++}} \end{array}$


Conjunto solução:  $\mathtt{S=]-4/3~, 1]}$


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