Solve $|1 + x| < 1$ I'm trying to solve $|1 + x| < 1$. The answer should be $ -2 < x < 0$ which wolframalpha.com agrees with.
My approach is to devide the equation to:
$1+x < 1$ and $1-x < 1$ and then solve those two:
$ 1+x < 1 $
$ x < 0 $
$ 1 - x < 1$
$ -x < 0$
$x > 0$
And this gives me $ x = 0$. Where am I going wrong?

Every exercise dealing with $| \cdot |$ can be solved as follows:
\begin{align}|1+&x| < 1 \\
(\iff) -1 < 1&+x < 1 \\
(\iff) -2 < &x < 0
\end{align}
