inequalities question (1 Viewer)

[Kyroth***]

Ok, simple question...
x2 < 1
(that's x squared less than one)
So sue me, I suck at inequalities.
Is it -1<x<1, or is there another rule? I can't find a text book explaining it...

 

[Kyroth***]

And for some reason not all of that came out... I meant to say, it is -1 < x < 1, or is there another rule for this, because my text book won't tell me.

 

[Dreamerish*~]

x² < 1

I always do these things by logic, which I probably shouldn't.

The answer is -1 < x < 1 because any number less than 1 squared is less than 1 because it's a decimal.

 

[acmilan]

It basically comes from the fact that:

sqrt(x²) = |x|

so:

x² < 1
sqrt(x²) < sqrt(1)
|x| < 1

and |x|<1 is, by definition -1 < x < 1

 

[Kyroth***]

cool, thanks

 

[Trev]

You can figure it out graphically, just look at the graph of y=x² and see where the graph lies less than y=1.