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Solving Absolute Value Inequalties with Less Than

Still have your fingers in your ears?  Good!

Check out this guy:

| blob | is less than or equal to 3
 

A number line showing solid dots at -3 and 3 connected by a solid line ... Mr. blob has got to live in here!

-3 < blob < 3

So, what about this?

Solve       | x + 2 | is less than or equal to 3


A number line showing that x + 2 lives between -3 and 3

Set it up!

-3 is less than or equal to x + 2 is less than or equal to 3 ... Solve it! ... subtract 2 from all three parts ... -5 is less than or equal to x is less than or equal to 1

 

interval notation [ -5 , 1 ] That's it!