SOLUTION: What is the value of x in the equation 2 over x minus 3 equals 26 over x? I looked at the answer key and it said it was -8, but can you explain to me why? Truly appreciate it

Algebra ->  Proportions  -> Lessons -> SOLUTION: What is the value of x in the equation 2 over x minus 3 equals 26 over x? I looked at the answer key and it said it was -8, but can you explain to me why? Truly appreciate it      Log On


   

Question 607326: What is the value of x in the equation 2 over x minus 3 equals 26 over x?
I looked at the answer key and it said it was -8, but can you explain to me why?
Truly appreciate it! Thanks!
Found 2 solutions by ewatrrr, Nihal@SriLanka:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

%282%2Fx%29+-3+=+26%2Fx   |Multiplying thru by x so as all denominators = 1

   2 - 3x = 26  |Adding 3x and Subtracting 26 from both sides of the EQ

    -24 = 3x

      -8 = x

Answer by Nihal@SriLanka(22) About Me  (Show Source):
You can put this solution on YOUR website!
[2/(x-3) = 26/x
multiplying both sides by x(x-3) we have
2x = 26(x-3)
i.e. 2x = 26x-26.3
i.e.-24x= -78
i.e. x = 3.25
either the answer key is wrong or you have stated the problem erroneously]


Since publishing the above solution I have noted another solution being offered giving the intended answer. For the benefit of the original queror or other interested persons it is good to note down why the above solution did not produce the intended answer.

The original question is somewhat ambiguous - '2 over x minus 3' could be interpreted as either '2 over (x-3)' or '(2 over x) minus 3'.
only the latter interpretation will give the intended answer.
The former interpretation being used in the above solution it does not yield the same result.

Again for the benefit of the average reader who is not very conversant with the relevant rules it is good to point out that in an arithmatical/mathematical expression, division/multiplication has precedence over addition/subtraction operations. No such rule applies to an English language expression which '2 over x minus 3' is. Hence the ambiguity. It is important that such ambiguities are avoided by proper use of language in language expressions and appropriate use of parentheses in arithmatical/mathematical expressions.

for any clarification you may email sumanapala@gmail.com