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### 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

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/
```
Associated Topics:
High School Basic Algebra

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