How do you solve and write the following in interval notation: #| x | – 2 <7#?

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Answer 1 · 2016-06-25T20:00:12

First of all we write

#|x|-2<7#

#|x|<9#

then we remove the absolute value remembering that we have to use both signs #\pm# and when we use the #-# sign we have to invert the inequality.

#|x|<9#

#x<9# and #x> -9#

This tell us that #x# can assume any value between #-9# and #9# that can be written as

#-9 < x < 9#
or
#x\in(-9,9)#.