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
enter image source here

Related questions
See all questions in Multi-Step Equations with Like Terms
Impact of this question
1375 views around the world
You can reuse this answer
Creative Commons License