How do you solve and write the following in interval notation: #|x + 3| < 12#?

1 Answer
Roy Ø.
May 6, 2018

#-15<x<9# or #x in(-15,9)#

Explanation:

To solve this we have to understand what |x+3| means, namely the absolute value of (x+3). That means (x+3) must have a value between -12 and +12, so
#-12<(x+3)<12#
But for #-12<(x+3)# we must have #-15<x#.

And for #x+3<12# we must have #x<9#

Therefore it follows that #-15<x<9#.

Which also can be written as #x in(-15,9)#

Graphically
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