Question

(5x+2)(2-x)(4x+3)>0 resolucao

Answer 1

f(x)=5x+2

$5x+2=0\rightarrow\,x=-\dfrac{2}{5}$

$f(x)>0\,se\,x>-\dfrac{2}{5}\\f(x)\textless0\,se\,x\textless-\dfrac{2}{5}$

g(x)=2-x

$2-x=0\\x=2$

$g(x)>0\,se\,x\textless2\\g(x)\textless0\,se\,x>2$

h(x)=4x+3

$4x+3=0\rightarrow\,x=-\dfrac{3}{4}$

$h(x)>0\,se\,x>-\dfrac{3}{4}\\h(x)\textless0\,se\,x\textless-\dfrac{3}{4}$

Montando o quadro sinal e assinalando a resposta temos

$\mathsf{s=\{x\in\mathbb{R}/-\dfrac{3}{4}\textless\,x\textless-\dfrac{3}{5}\,ou\,x>2\}}$