How do you solve #|x| <3#?

1 Answer
Sep 4, 2016

Answer:

You have to use the definition of #|x|#:
#|x|=x#, if #x>=0#
#|x|=-x#, if #x<0#

Explanation:

So we first consider #x>=0#. In this case #|x|=x#, and the inequality becomes #x<3#. Hence, all #x# such that #x>=0# and #x<3# satisfy the inequality. That is all #x#, #0<=x<3#

Now consider #x<0#; is this case #|x|=-x#, and the inequality becomes #-x<3#. This is the same as #-3 < x#, so all the #x# such that #-3 < x < 0# satisfy the inequality.

Putting both together, the solution are all #x# such that #-3 < x <3#