Question 741714: Dear Sir/Madam,
I do not know how to do this question:
|3x-5|=3x-5
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176)   (Show Source):
Answer by ikleyn(53201)  (Show Source):
You can put this solution on YOUR website! .
Dear Sir/Madam,
I do not know how to do this question:
|3x-5|=3x-5
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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.
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 ANSWER is
+------------------------------------------------------------------------------------+
| Equation |3x-5| = 3x-5 has infinitely many solutions in the domain x >= 5/3. |
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| All x's in this domain are the solutions to this equation. |
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| In the domain x < 5/3, equation |3x-5| = 3x-5 has no solutions. |
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| Thus, the solution set for the given equation is { x | x >= 5/3 }. |
+------------------------------------------------------------------------------------+
Solved completely.
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