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Coolmath Algebra
Solving Absolute Value Equations and Inequalities Lesson 3 -
Solving Absolute Value Inequalities with Less Than (page 1 of 4)
---- This algebra lesson explains how to solve absolute value inequalities that have "less than" signs

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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 3 is

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!

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
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