Thread: how to solve this inequality

[4 / (1 - x)] < 2

Originally Posted by marie7

[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 $\displaystyle x<-1$