Question 741714
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Dear Sir/Madam,
I do not know how to do this question:
|3x-5|=3x-5
~~~~~~~~~~~~~~~~~~~~~~~~~



        Dear visitor,


        first what I have to say,  looking at your post,  is that there is  NO  question in it.

        There is some equation,  but there is no question.

        So,  in order for this post makes sense,  I/we should create a question to it.


        One reasonable question is  " Find the set of solutions to this equation. "


        So,  I will assume that this is the question,  and I will give the solution in my post below.



<pre>
Function  y = |3x-5|  has two branches.


(1)  At x >= 5/3,  this function is y = 3x-5,  and it coincides with the function 3x-5 in the right side 
     of the given equation.


     So, in the domain  x >= 5/3,  the given equation,  |3x-5| = 3x-5  has infinitely many solutions
     that are the entire set  { x | x >= 5/3 }.



(2)  At x < 5/3,  this function y = |3x-5|  is positive,  while  3x-5  is negative.

     Therefore, in the domain x < 5/3,  the given equation has no one solution.


At this point, the analysis is complete.  The <U>ANSWER</U>  is


    +------------------------------------------------------------------------------------+
    |   Equation  |3x-5| = 3x-5  has infinitely many solutions in the domain  x >= 5/3.  |
    |                                                                                    |
    |   All x's in this domain are the solutions to this equation.                       |
    |                                                                                    |
    |   In the domain  x < 5/3,  equation  |3x-5| = 3x-5  has no solutions.              |
    |                                                                                    |
    |   Thus, the solution set for the given equation is  { x |  x >= 5/3 }.             |
    +------------------------------------------------------------------------------------+
</pre>

Solved completely.