What am I doing wrong?

|2x+1|<|x+3| Solve for x.

So the correct answer is -4/3<x<2 based on my deductions. But my problem is my solution generates more answers.

+-(2x+1)<+-(x+3) =>

1) 2x+1<x+3 => x<2

2) 2x+1<-(x+3) => x<-4/3

3) -(2x+1)<(x+3) =>x>-4/3

4) -(2x+1)<-(x+3) => x>2

What am I doing wrong in the solution to get 2), 4) as wrong answers. I know I am probably having a brain fart and missing something obvious.

Thanks in advance for your help.