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Negative number

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Hi ,
The variable x is not necessarily positive, nor is - x necessarily negative.
Why cannot state - x is a negative number?

And also If x = -y, then we have either
x 0 y or y 0 x in a number line
Why Can't we determine just as - y is a negative number with a sign?

This is from Manhattan Number Properties.

Pls Help me!

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