Question

решите неравенство х(7х-3)/4-2х меньше 0

Answer 1

$\ frac{x(7x-3)}{4-2x}<0\ frac{x(7x-3)}{4-2x}=0Rightarrow x(7x-3)=0Rightarrow x=0, 7x-3=0Rightarrow x=frac37\ xin(-inty,0)cup(0,frac37)cup(frac37,+infty)\xin(-infty,0): x=-1Rightarrow frac{x(7x-3)}{4-2x}=frac{-1(7(-1)-3)}{4-2(-1)}=frac{10}6>0\xin:(0,frac37) x=0,1Rightarrow frac{x(7x-3)}{4-2x}=frac{0,1(7cdot0,1-3)}{4-2cdot0,1}=-frac{0,23}{3,8}<0\xin:(frac37,+infty) x=1Rightarrow frac{x(7x-3)}{4-2x}=frac{1(7cdot1-3)}{4-2cdot1}=2>0\Rightarrow xin:(0,frac37)$