Question 1199373
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I will answer exactly as you ask in your post.



Your first step setup  is incorrect.


The correct first step should be as follows


<pre>
    x + |3x-2| = 2  or  x + |3x-2| = -2.
</pre>

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.
</pre>


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As the next step, &nbsp;you should consider two cases:


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a)  &nbsp;&nbsp;3x-2 >= 0,   &nbsp;&nbsp;&nbsp;&nbsp;and


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b)  &nbsp;&nbsp;3x-2 < 0.



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I just answered your questions.


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


These lessons are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-1.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-2.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/absolute-value/HOW-TO-solve-equations-containing-Linear-Terms-under-Abs-Value-sign-L-3.lesson>HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3</A>


It is the material for you to learn from.