Spivak Calculus 3rd Edition Chapter 1 Problem 4 (iii) I'm not sure on arriving at the solution to $5-x^2 < -2$ .  I've got:
$5-x^2 < -2$
$-x^2 < -7$
$x^2 < 7$
$\sqrt x^2 < \sqrt 7$
$x < \sqrt 7$
But the actual solution is $x > \sqrt7$ or $x < -\sqrt7$ 
Can someone point me in the right direction on this, thanks.

Note that
$$
-x^2 < -7\iff x^2> 7\iff|x|>\sqrt{7}.
$$
In the first step multiplying both sides of the inequality by $-1$ "flips" the inequality sign.
