How do you solve and write the following in interval notation: #x>=12# or # x<-4#?

1 Answer
Oct 12, 2017

Answer:

#x in[12,oo)# and #x in(-oo,-4)#

Explanation:

Lets take your question as an example.

We have #x>=12#

This means the value of #x# can be #12# or greater than #12# up to #oo#.

So the interval notation for this will be #x in [12,oo)#

Here, this [ ] bracket means its a closed interval. This means #x# will include all the values in the bracket.
( ) bracket means an open interval, #x# will include the values in the bracket other than the ones on the extreme ends.

So when we write #x in [12,oo)# we say that #x# can be ranging from #12# to #oo# where #12# is included and #oo# is not.

Similarly #x<-4# says #x# has to be less than #-4# and cannot be greater than or equal to #-4# . In interval notation
It can be written as #x in(-oo,-4)#

Its an open interval on both sides because #x# can be all the values in between #-oo# and #-4# but cannot be #-oo# or #-4#