Solving Absolute Value Functions

Date: 07/19/98 at 23:56:11
From: Rich 
Subject: Absolute Value Problems

How do you solve |4/7x + 6| + 3 = 15?

Date: 07/21/98 at 15:57:25
From: Doctor Margaret
Subject: Re: Absolute Value Problems

Hi Rich,

Thanks for writing to us. This equation actually has to be solved 
twice because of the absolute value. The absolute value of a number is 
its distance from zero on the number line. Distance is always a 
positive number or zero, so the absolute value of a number is always a 
positive number or zero. The distance from 0 to 3 on the number line 
is three units and the distance from -3 to 0 is also three units. 
Thus:  

   |3| = 3    and    |-3| = 3

To solve an equation containing an absolute value sign, remove the 
sign and rewrite it as two equations. For example:

   |x + 2| = 8 

turns out to be:

   x + 2 = 8    and   -(x + 2) = 8
   x = 6              -x - 2 = 8     <-- distribute the negative
                      -x = 10            on the entire 
                      x = -10            expression   

So the answers are 6 and -10.  Plugging them back into the equation:

   |6 + 2| = 8   and      |-10 + 2| = 8
   |8| = 8                |-8| = 8

These two answers are correct.  

Now it's your turn to try. Let me know how you did, or if you need 
more help.                                                     

- Doctor Margaret, The Math Forum
Check out our web site! http://mathforum.org/dr.math/