Algebra - Request explanation

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Algebra - Request explanation

by vzzai » Fri Apr 08, 2011 8:07 pm
If x^2 - 9 < 0, which of the following is true?
1) x<-3
2) x>3
3) x>9
4) x<-3 or x>3
5) -3<x<3

I could arrive at (x+3)(x-3) < 0, and I understand that one of them need to be negative and another positive. But I'm unable to take a step forward to arrive at the solution. Could you help with the explanation?[spoiler][/spoiler]

Source: Kaplan
Thank you,
Vj
Source: — Problem Solving |

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by Tani » Fri Apr 08, 2011 8:42 pm
rather than factoring, simply add 9 to each side. The equation then reads x^2 <9.
Since x^2 is always positive, our x can be either positive or negative as long as its absolute value is less than three. Therefore 5) -3<x<3 is correct
Tani Wolff