Absolute Value Equations

The absolute value of a number is the distance the number is from zero on a number line.  Since distance is ALWAYS positive, the absolute value of a nonzero number can never be negative.

Examples:

 |4| = 4 is read "the absolute value of four equals four"

 |-9| = 9 is read "the absolute value of negative nine equals nine"

 

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Let's try some!

Ex:   Solve   |y - 10| = 12

You know that there are two cases we can have:  

the number (y-10) can equal positive 12 and the number (y-10) can equal -12.  

So...

1. y - 10 = 12  
2. y - 10 = -12

Solve BOTH for y!

The solutions are y = 22 and y = -2.

 

 

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