How to calculate range of x in inequality equations with MOD

is |x+1|<2?

1. (x-1)^2<1
2. x^2-2<0

I need to understand reason behind why some approaches are not yielding the right range of x when i am trying to simplify the questions.

first approch:
[x+1]<2
(x+1)^2 <4
X^2+2x+1 <4
(x+3)(x-1)<0
X+3<0
x-1<0
x<-3
x <1
WRONG result

2)[x+1]<2
(x+1)^2 <4
X^2+2x+1 <4
X(x+2) <3
X<3
X<-1
WRONG RESULT

3)[x+1]<2
(x+1)^2<4
Taking root on both sides
(x+1)<2 ; (x+1)<-2
X<1; x<-3
WRONG RESULT

4)[x+1]<2
X+1 = y
|y|<2
-2<y<2
-2<x+1<2
-3<x<1
CORRRECT RESULT

5) [x+1]<2
X+1 <2
-(x+1)<2
X<1; x>-3

CORRECT Result

SO I need to understand why the first three approach are not giving me right range???what am I doing wrong. Please explain the underlying concept between modulus/squares/roots.

Thank you,

Regards,
ABhi