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Solving "Greater Than" Absolute Value Inequalities - Concept

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 "Greater Than" Absolute Value Inequalities

We're going to talk about when we're dealing with an Absolute Value that is greater than a number okay? So in this case we're looking at Absolute Value of x is greater than 3, so think about some examples of where this will work okay? We need a number where when it take in the Absolute Value if it's taken of it it's going to be greater than 3, so if we're thinking positive numbers x=4 Absolute Value of 4 is 4, 4 is greater than 3. What if we went to negative numbers x is equal to let's say -6 okay? Absolute Value of -6 is actually positive 6, 6 is greater than 3.
When we're dealing with an Absolute Value that is greater than something we're actually going to end up with two different regions okay? And what I always remember for this is Absolute Value is greater, there's a little thing I like to remember which is great tor, great tor, or as an a union it's one or the other okay? So what we actually make up for this is two different statements this can go to x is greater than 3 obviously cause it's just the same thing that's here or x is and then you just want to flip the sign and flip the number less than -3 okay? So if you think about this, this is going to be numbers that are further down the number line take the Absolute Value of that it's actually going to be bigger than 3 this is the dealing with this, so we actually what we end up with is a union I'm on another representation here is 3 here is -3 the numbers that will satisfy it are on either extreme.
The [IB] negative, so you're turning into a or statement, another way of looking at this is the union between these two things. Whenever you're dealing greater remember union great tor.

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