SOLUTION: Good day.Could you please hape me to solve this question.I lernt the wey of your answers but I can not receive to the same answer as the lecture note. Dan said Jeff:"I'm thinkin

Algebra ->  Algebra  -> Equations -> SOLUTION: Good day.Could you please hape me to solve this question.I lernt the wey of your answers but I can not receive to the same answer as the lecture note. Dan said Jeff:"I'm thinkin      Log On

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Question 201635: Good day.Could you please hape me to solve this question.I lernt the wey of your answers but I can not receive to the same answer as the lecture note.
Dan said Jeff:"I'm thinking of a certain fraction whose denominator is 1 less than twice its numerator.If I add 7 to both its numerator and its denominator,I obtain the number 3%2F4. What is the fraction of which I'm thinking?
This is my way :%28x%2B7%29%2F%282x-1%2B7%29=3%2F4+ So: %28x%2B7%294=%282x%2B6%293
This was the solver way:%28x%2B7%29%2F%282x-1%2B7%29-3%2F4=0
I always use of the first way but now I'm not sure about that!
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(28598) About Me  (Show Source):
You can put this solution on YOUR website!
You have the correct equation (and the solver has an altered form of your equation), so let's take it from there...



%28x%2B7%29%2F%282x-1%2B7%29=3%2F4+ Start with the given equation.


%28x%2B7%29%2F%282x%2B6%29=3%2F4+ Combine like terms.


4%28x%2B7%29=3%282x%2B6%29 Cross multiply


4x%2B28=6x%2B18 Distribute.


4x=6x%2B18-28 Subtract 28 from both sides.


4x-6x=18-28 Subtract 6x from both sides.


-2x=18-28 Combine like terms on the left side.


-2x=-10 Combine like terms on the right side.


x=%28-10%29%2F%28-2%29 Divide both sides by -2 to isolate x.


x=5 Reduce.


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Answer:

So the solution is x=5

This means that the fraction x%2F%282x-1%29 becomes 5%2F%282%2A5-1%29=5%2F9


So the original fraction was 5%2F9


Take note that %285%2B7%29%2F%289%2B7%29=12%2F16=3%2F4 which verifies our answer.



Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
I'm thinking of a certain fraction whose denominator is 1 less than twice its numerator.If I add 7 to both its numerator and its denominator,I obtain the number 3/4. What is the fraction of which I'm thinking?
--------------------
Original = x/(2x-1)
Add 7 --> (x+7)/(2x+6)
(x+7)/(2x+6) = 3/4
Cross multiply
4(x+7) = 3(2x+6)
4x+28 = 6x+18
2x = 10
x = 5
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Original = 5/9
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Adding 7's --> 12/16 = 3/4
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Note that 5/9 is the smallest positive number that satisfies the conditions. There are an infinite number of solutions, eg
17/25, 293/393, 1193/1593, etc.
Multiply 3/4 by any factor and subtract 7's from the result.
Even -1/1 fits.