Spivak Calculus 3rd Edition Chapter 1 Problem 4 (iii)

by Algebrator   Last Updated January 12, 2018 22:20 PM

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 $x > \sqrt7$

Can someone point me in the right direction on this, thanks.

Tags : inequality


Answers 1


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.

Foobaz John
Foobaz John
January 12, 2018 22:16 PM

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