[4 / (1 - x)] < 2
$\displaystyle \frac{4}{1-x} < 2$
$\displaystyle \frac{2}{1-x} < 1$
$\displaystyle \frac{2}{1-x}-1<0$
$\displaystyle \frac{1+x}{1-x} < 0$
Case 1: $\displaystyle 1+x>0$ and $\displaystyle 1-x<0$
$\displaystyle x>-1$ and $\displaystyle x>1$
ie $\displaystyle x>1$
Case 2: $\displaystyle 1+x<0$ and $\displaystyle 1-x>0$
$\displaystyle x<-1$ and $\displaystyle x<1$
ie $\displaystyle x<-1$