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### Absolute Value: Consider Two Cases

```
Date: 08/21/97 at 13:27:59
From: Mandy Pedro
Subject: Algebra 2

I am having problems with this one section in my Algebra 2 course. It
is about absolute value and they tell you to solve the equation. Here
is a example: |7+3a| = 11-a .

Thank you a lot.
```

```
Date: 08/27/97 at 12:03:24
From: Doctor Rob
Subject: Re: Algebra 2

To solve equations like |7 + 3*a| = 11 - a, you have to consider two
cases.  Recall |x| = x if x >= 0, and |x| = -x if x < 0.

Case 1: 7 + 3*a >= 0, which can be rewritten as  a >= -7/3.
Then you are solving 7 + 3*a = 11 - a, which yields a = 1.
Remember to check that your answer still satisfies the
condition a >= -7/3 (it does).

Case 2: 7 + 3*a < 0, which can be rewritten as a < -7/3.  Then you
are solving -(7 + 3*a) = 11 - a, which yields a = -9.
Again, we must remember to check that -9 < -7/3 (it is).

Thus there are two answers:  a = 1 and a = -9.

Most problems of this type are handled in a similar way.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

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