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Set Operation: Intersection - 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!

Solving an intersection of inequalities. Here we have two pretty simple inequalities that we’re looking for the intersection for. We don’t have anything to solve for, so for this I would just jump straight to a number line.

Draw a number line out. This right there is saying x is greater than 4. We have our 4, and here we’re dealing with open circle, because we’re not equal to, everything greater than that. X is less than -1, open circle, goes down.

We’re looking for the intersection; we’re looking for where these two things overlap. Here everything is less than -1; here everything is greater than 4. Is there really any overlap? Can we get one number that is both less -1 and greater than 4. Not really. Doesn’t make sense, and our number line shows that, that there’s really no place that these two things overlap.

There is no intersection; no number can satisfy both of these two statements, so therefore we have no intersection.

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