Question

Determine o conjunto solução da inequação (6+3x)(3-x)<0

Answer 1

    $(6+3x)(3-x)<0$

Cálculos auxiliares:

    $(6+3x)(3-x)=0\Leftrightarrow$

$\Leftrightarrow 6+3x=0\;\vee\;3-x=0\Leftrightarrow$

$\Leftrightarrow 3x=-6\;\vee\;-x=-3\Leftrightarrow$

$\Leftrightarrow x=-2\;\vee\;x=3$

$x\hspace{15mm}|-\infty\hspace{10mm}|\hspace{1mm}-2\hspace{1mm}|\hspace{15mm}|\hspace{1,75mm}3\hspace{1,75mm}|\hspace{10mm}+\infty$

$6+3x\hspace{7mm}|\hspace{7mm}-\hspace{7mm}|\hspace{3mm}0\hspace{3mm}|\hspace{5mm}+\hspace{5mm}|\hspace{1mm}+\hspace{1mm}|\hspace{10mm}+$

$3-x\hspace{8,5mm}|\hspace{6,9mm}+\hspace{6,9mm}|\hspace{2mm}+\hspace{2mm}|\hspace{5mm}+\hspace{5mm}|\hspace{2,5mm}0\hspace{2,5mm}|\hspace{10mm}-$

$f(x)\hspace{10mm}|\hspace{6,9mm}-\hspace{6,9mm}|\hspace{3mm}0\hspace{3mm}|\hspace{5mm}+\hspace{5mm}|\hspace{3mm}0\hspace{3mm}|\hspace{10mm}-$

Resposta:  $x\in\;]-\infty\:;\:-2[\;\cup\;]3\:;\:+\infty[$