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Solving Absolute Value Inequalties with Less Than

Remember that an absolute value is a distance away from zero on a number line:

| x | = 3 ... What numbers ( x ) ... have a distance ( | | ) ... of 3? ( 3 )

 

a number line showing that the distance between -3 and 0 is 3 ... the distance between 3 and 0 is 3

x = -3 or x = 3


So, what about this guy?

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

All these! ... A number line showing closed dots at -3 and 3 with a solid line connecting them

So, get this in your head:

The solution to | x | is less than or equal to 3is

A number line showing closed dots at -3 and 3 with a solid line connecting them

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

If you have to, stick your fingers in your ears to keep it in there!  This baby will pop up on you again and again in statistics and Calculus!