Question

resolva, nos R, a inequação: x+4 / 6x+9 ≤ 0​

Answer 1

$\large\boxed{\begin{array}{l}\rm Resolva,nos~\mathbb{R},~a~inequac_{\!\!,}\tilde ao~\dfrac{x+4}{6x+9}\leqslant0\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao\!:} \\\sf fac_{\!\!,}amos~f(x)=x+4~e~g(x)=6x+9\\\sf e~estudemos~o~sinal~de~cada~uma~separadamente.\\\underline{\tt para~f(x)\!:}\\\sf f(x)=x+4\\\sf c\acute alculo~da~ra\acute iz:~x=-\dfrac{4}{1}=-4\\\sf f(x)>0~se~x>-4~e~f(x)<0~se~x<-4\\\rm observe~o~anexo~para~concluir~isso.\end{array}}$

$\boxed{\begin{array}{l}\underline{\tt para~g(x)\!:}\\\sf c\acute alculo~da~ra\acute iz:~x=-\dfrac{9}{6}=-\dfrac{3}{2}\\\sf g(x)>0~se~x>-\dfrac{3}{2}~e~g(x)<0~se~x<-\dfrac{3}{2}\\\rm observe~o~anexo~para~concluir~isso.\end{array}}$

$\large\boxed{\begin{array}{l}\sf Agora~monta-se~o~quadro~sinal~para~finalizar~a~quest\tilde ao\\\sf observe~que~os~valores~de~x~que~est\tilde ao~entre~-4~e~-\dfrac{3}{2}\\\sf incluindo~-4~e~excluindo~-\dfrac{3}{2}~\\\sf satisfazem~a~inequac_{\!\!,}\tilde ao~proposta.\\\sf portanto~S=\bigg\{ x\in\mathbb{R}/-4\leqslant x<-\dfrac{3}{2}\bigg\}\end{array}}$