SOLUTION: How on earth do you prove that: |x|=|-x| And |x|≥0 Just seems so hard to prove it?

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Question 1018501: How on earth do you prove that:
|x|=|-x|
And
|x|≥0
Just seems so hard to prove it?
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
How on earth do you prove that:
|x|=|-x|
----------------------------------- 

1.  Let x be a non-negative real number: x >= 0.

    Then |x| = x.

    Also then -x is negative number, and |-x| = -(-x) by the definition of the modulus. So, |-x| = -(-x) = x.

    Thus we proved that if x >= 0, then  |x| = |-x|.


2.  Now consider the case, when x is negative real number: x < 0.

    Then |x| = -x by the definition of the modulus.

    Also then -x is positive number, and hence |-x| = -x.

    Thus we proved that if x < 0, then  |x| = |-x|.


Thus we proved that in all cases |x| = |-x|.

QED.