Solve the following equation?

Question

#||x-2|-3|<5#

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Answer 1 · 2018-07-28T17:22:07

#-6 < x < 10#

#||x-2|-3|<5# means

either #|x-2|-3<5# i.e. #|x-2|<8#,

which means #x-2<8# i.e. #x<10#

or #x-2> -8# i.e. #x> -6#

which implies #-6 <x< 10#

or #|x-2|-3> -5# i.e. #|x-2|> -2#

but this always true.

Hence answer is #-6 < x < 10#