How do you solve and write the following in interval notation: #-4<1/x<= 1 #?

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Answer 1 · 2018-07-17T14:14:21

We get #(-infty,1/4)# or #[1,\infty)#

We are doing case work to solve this inequality:

a) #x>0#
in this case we multiply the given inequality by #x# and we get

#-4x<1# and #1<=x#

so we have #x > -1/4# and #x>=1# so we get #x>=1# in this case.

b)#x<0#
we multiply by #x<0#

so we get

#-4x>1>=x#

solving this we get

#x<-1/4# and #x<=1#

so we get the solution

#x<-1/4#