Question

Quantas soluções inteiras tem a inequação (2x+4)/(6-2x)>0?
a) 3
b) 4
c) 5
d) 6
e) 7​

Answer 1

$\sf{\dfrac{\underbrace{2x+4}_{f(x)}}{\underbrace{6-2x}_{g(x)}}\textgreater0}$

$\sf{f(x)=2x+4}\\\sf{f(x)=0\implies 2x+4=0}\\\sf{x=-\dfrac{4}{2}=-2}\\\sf{f(x)\textgreater0\implies x\textgreater-2}\\\sf{f(x)\textless0\implies x\textless-2}\\\sf{g(x)=6-2x}\\\sf{g(x)=0\implies 6-2x=0}\\\sf{x=-\dfrac{6}{-2}=3}\\\sf{g(x)\textgreater0\implies x\textless3}\\\sf{g(x)\textless0\implies x\textgreater3}$

Montando o quadro sinal(veja anexo) e assinalando a resposta temos

$\sf{S=\{x\in\mathbb{R}/-2\textless x\textless3\}}$

Vamos exibir os inteiros compreendidos entre -2 e 3.

$\boxed{\boxed{\boxed{\boxed{\sf{\{-1,0,1,2\}}}}}}$

Portanto temos 4 soluções inteiras

$\huge\boxed{\boxed{\boxed{\boxed{\sf{\maltese~~alternativa~~b}}}}}$