How do you solve #absx>=x#?

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1 Answer
George C.
May 24, 2015

With moduli, it is often helpful to split into cases at the point where the enclosed value changes sign.

Case (a): #x >= 0#
If #x >= 0# then #|x| = x >= x#.
So all #x >= 0# satisfy #|x| >= x#.

Case (b): #x < 0#
If #x < 0# then #|x| >= 0 > x#.
So all #x < 0# satisfy #|x| >= x#.

Combining the two cases we find #|x| >= x# is satisfied for all #x in RR#

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