Question 22941: 2/3x-5=x
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Do you mean 
If so, then cross multiply (or equivalently multiply both sides by the denominator (3x-5) ).
This is quadratic, so set equal to zero by subtracting 2 from both sides:
Fortunately the trinomial factors (or you can use the quadratic formula!):
Set each factor equal to zero:
3x+1=0
3x=-1
x=-1/3
x-2= 0
x=2
Neither answer makes a denominator zero, so both answers are acceptable.
On the other hand suppose the solution were intended to be
Now the LCD is 3x, so multiply both sides by 3x:
This would best be solved by the quadratic formula  , since it does not factor:
 Ugly, but that's life!
Then again, maybe the problem was intended to be  . Now the LCD is just 3, so you can multiply both sides of the equation by 3:
Subtract 2x from each side:
Now that's better!! Do you see why it is SO important to state your problems clearly? Remember that EVERYONE at algebra.com uses the same order of operations agreement (including students, right?), and it really helps if in doubt to put parentheses around denominators and quantities inside radicals, etc. That way we ALL know what you mean in the problem.
As you can see, this one problem had THREE interpretations, and THREE different answers!! Help us out by stating your problem clearly!!
R^2 at SCC
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