Question 1014976: I am working on solving inequalities and then writing them in interval notation. I am fine with solving and writing the inequalities with the word 'and" in interval notation. I am struggling with writing inequalities with the word "or" in interval notation. My question is how come a problem such as X<2/3 or X>-1/2 can be simplified into interval notation as (-infinity, infinity) but X+4<0 or 6x>-12 is written as (-infinity,-4) U (-2,infinity)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! X<2/3 includes -1/2 and x>-1/2 includes 2/3, hence the open interval (-infinity, infinity)
:
x+4<0
x<-4
:
6x>-12
x>-2
:
there is no overlap between these two inequalities, x<-4 or x>-2, therefore
(-infinity,-4) U ((-2,infinity)
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