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Solving Absolute Value Inequalties with Greater Than

Don't worry, there are only 5 more types...

Heh, just kidding.  There's only one more.

We've already learned how to do these:

| x | = 3 and | x | is less than or equal to 3

x = -3 or x = 3               -3 is less than or equal to x is less than or equal to 3

Here's the last kind we need to worry about:

| x | is greater than or equal to 3 ... What numbers ( x ) ... have a distance ( | | ) ... greater than or equal to 3? ( 3 )

A number line indicating the solution must be less than or equal to -3 or greater than or equal to 3

 

     Which is           x is less than or equal to -3 or x is greater than or equal to 3

 

This is REALLY different from the other two types...  and you need to get all of them memorized.  Flash card time.  I highly suggest that you have your flash cards laminated -- then you can take them into the shower with you!