What is the solution to the inequality #absx > 6#?

1 Answer
KillerBunny
May 13, 2018

#x>6# or #x<-6#

Explanation:

If you consider any number #x>6#, the inequality is trivially solved: you have #|x|=x#, and you're choosing a number bigger than #6# in the first place.

If instead you consider some number #x<-6#, then #|x|=-x#, and so you go back to the first case

For example, if you choose #x=17# you're in the trivial case: #|17|=17#, and #17>6#.

If instead you choose #x=-20#, you have #|-20|=20#, and #20>6#.

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