Show that for every x in R , 0<=|x|-x<=2|x|
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Show that for every x in R , 0<=|x|-x<=2|x|

[From: ] [author: ] [Date: 12-04-30] [Hit: ]
|x|-x = x - x = 0.Done.......
hello
help me please!

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To show that |x| - x >= 0, we just note that |x| >= x always.

To show that |x|-x <= 2|x|, we can break it into 2 cases:

Case 1: x >= 0. Then |x| = x, and so:

|x|-x = x - x = 0.

and clearly 0 <= 2|x|, so we are done.

Case 2: x < 0. Then |x| = -x, and so:

|x|-x = -x -x = 2x <= 2|x|

Done.
1
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