question about inequalities with negative numbers and square roots

let's say you have an inequality such as this:

-1< -2x² < 1 and it reduces to 1/square root of 2 > x > -1/square root of 2

I understand why the inequalities can flip around but I forgot why you don't end with an imaginary number due to taking
the square root of a negative number.

Quote:

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Originally Posted by matnov

let's say you have an inequality such as this:
-1< -2x² < 1 and it reduces to 1/square root of 2 > x > -1/square root of 2

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Note that can be written as so .

thank you, I think I understand. great site by the way - but can anyone refer me to some free software that will let me post mathematical notation on this forum? thanks

Quote:

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Originally Posted by matnov

thank you, I think I understand. great site by the way - but can anyone refer me to some free software that will let me post mathematical notation on this forum? thanks

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It is LaTeX. Go to the LaTeX subforum.