Solve the inequality $|x^2-2|<1$ I'm trying to solve inequalities that include absolute values. The way we solved these questions in class is different than what I am used to. The teacher would take the positive and negative possibilities of the inequality and treat them separately. I am trying to solve this as a union of intervals.
$$|x^2-2|<1$$
Normally I would just write this as:
$$-\sqrt{3} < x < -1 \text{ and } 1 < x < \sqrt{3}$$
However this is not correct I don't believe.

$|x^2-2|<1$
$-1<x^2-2<1$
$1<x^2$ or $x^2<3$
$1<x$, $-1>x$, or $-\sqrt{3}<x<\sqrt{3}$
Therefore, 
$-\sqrt{3}<x<-1$ and $1<x<\sqrt{3}$
