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

1 Answer
Jul 24, 2016

Answer:

You have to use the definition of absolute value:

#|a|=a# if #a>=0#
#|a|=-a# if #a<0#

Explanation:

For example #|5|=5#, #|-5|=5# and #|0|=0#

Let's first consider #x>=0#. In this case #|x|=x#, and the inequality reduces to #x<3#. So, the solution are #all# the values #x# that satisfy both #x>=0# and #x<3#, that is #0<=x<3#

If #x<0#, then #|x|=-x#, and the inequality reduces to #-x<3#, and so # -3 < x #. Thus the solution are #all# the values #x# that satisfy # -3 < x <0#

Putting together both solutions we have # -3 < x < 3#, that is, the interval #(-3, 3)#