SOLUTION: Solve the absolute value equation. | x + |3x - 2| | = 2 Here is my set-up: | x + |3x - 2| | = 2 or | x + |3x - 2| | = -2 Is this the correct first step

Algebra ->  Equations -> SOLUTION: Solve the absolute value equation. | x + |3x - 2| | = 2 Here is my set-up: | x + |3x - 2| | = 2 or | x + |3x - 2| | = -2 Is this the correct first step      Log On


   

Question 1199373: Solve the absolute value equation.

| x + |3x - 2| | = 2


Here is my set-up:



| x + |3x - 2| | = 2 or | x + |3x - 2| | = -2


Is this the correct first step?


If so, what is the next step?

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

I will answer exactly as you ask in your post.


Your first step setup is incorrect.

The correct first step should be as follows 

    x + |3x-2| = 2  or  x + |3x-2| = -2.

Pay attention on how I take off the absolute value signs:
I take them off (very extreme absolute value signs), but I write in the right side +2 or -2.


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As the next step,  you should consider two cases:

        (a)   3x-2 >= 0,     and

        (b)   3x-2 < 0.


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                I just answered your questions.

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In this web-site www.algebra.com,  there is a group of lessons,  where I show/explain how to treat similar equations.

These lessons are
    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1
    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2
    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3

It is the material for you to learn from.