1. ## Modulus and inequalities

Solve this,
(|x|+1)/(|x|-1)<4

Is there anything wrong with this step,
|x|+1 < 4|x|-4 ??
Then, -3|x|<-5
|x|>5/3
x>5/3, x<-5/3

OR
when x<0
(-x+1)/(-x-1)<4
x<-5/3
when x>=0
x>5/3

But there is another solution of -1<x<1. How to get this out??

Thanks.

2. Question
$\frac{|x|+1}{|x|-1}<4$

Instead of multiplying by $|x|-1$, multiply by $(|x|-1)^2$ and you should obtain that missing solution when solving the equation.

This works because when multiplying by $|x|-1$, you reduce the equation to a linear equation, eliminating possible solutions.