Question

Решить неравенство
$| frac{2x}{x-3}+1| textless 2$

Answer 1

|(2x+x-3)/(x-3)|<2
|(3x-3)/(x-3)|<2
-2<(3x-3)/(x-3)<2
{(3x-3)/(x-3)>-2⇒(3x-3+2x-6)/(x-3)>0⇒(5x-9)/(x-3)>0⇒x<1,8 U x>3
{(3x-3)/(x-3)<2⇒(3x-3-2x+6)/(x-3)<0⇒(x+3)/(x-3)<0⇒-3<x<3
x∈(-3;1,8)