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.