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Set Operation: Union - Problem 3

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

The union of two linear inequalities this particular example is are even solved out for us but if it wasn’t we would solve each particular inequality just as we would any other inequality. So for this I always plot my answer on a number line.

So here we have x is greater than 4, we have the number 4, not equal to this so it's an open circle greater than. This one over here x is less than -1 so we have -1 and we are going down. Now remember that the union is what’s represented in either set. So looking at our number line if we are dealing with numbers less than negative, 1 that’s taken out by this inequality.

If we are dealing with numbers greater than 4, that’s dealing with this one over here. In the middle, this is region that’s sort of left away there’s neither of these inequalities covers this. So there’s no way to really write our answer as just one region because we do have two regions that we are dealing with.

So the only way to write our answer for this is just pretty much rewriting what we have up here. So we actually have form negative infinity to -1 solve properly because it’s not equal to it. Union of 4, to infinity because there is no overlap, there is no over way to combine these two regions into one so our answer is actually left with two regions the union of the two.

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