Problem Solving

Find the solution to the inequality :
2x+5
------------ <3
|x| +1

1.x < -2/5 or x > 1
2.x < -1 or x > 2/5
3.x < -2/5 or x > 2
4.x > -2/5 or x < 2
5.x > 1 or x < -1

Pleas tell what is the problem within my approach :-

I am considering two secanarios, one is X>=0 and other is X<0; X can not be zero because if X=0 , inequality doesn't stand correct.

FOR X>0 ;
2x+5
------------ <3
x +1
Solving this will give X>2

For X<0 i.e value of X as negative

-2x+5
------------ <3
x +1

Doubt 1:- IS the above expression true when X<0;
Dount 2:- If yes, then after solving this i am getting X>2/5, which is not a solution of this.

Where i am wrong in getting concept of inequality. Please explain