SOLUTION: If fifteen less than two times a number is divided by six more than the number, the result is four less than 9 times the reciprocal of that number. Find the number

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Question 114531: If fifteen less than two times a number is divided by six more than the number, the result is four less than 9 times the reciprocal of that number. Find the number
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = "a number"
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Break it down, write an expression for each phrase
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If fifteen less than two times a number
2x - 15
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"is divided by six more than the number,"
%28%282x-15%29%29%2F%28%28x%2B6%29%29
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The word "is" usually mean "=" in these type problems
"result is four less than 9 times the reciprocal of that number.
%28%282x-15%29%29%2F%28%28x%2B6%29%29 = 9*1%2Fx - 4
Or
%28%282x-15%29%29%2F%28%28x%2B6%29%29 = 9%2Fx - 4
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Find the number
Multiply equation by x(x+6) to get rid of the denominators
x(x+6)*%28%282x-15%29%29%2F%28%28x%2B6%29%29 = x(x+6)*9%2Fx - x(x+6)(4)
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Cancel the denominators and you have:
x(2x-15) = 9(x+6) - 4(x^2 + 6x)
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2x^2 - 15x = 9x + 54 - 4x^2 - 24x
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Arrange as a quadratic on the left:
2x^2 + 4x^2 - 15x - 9x + 24x - 54 = 0
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6x^2 - 54 = 0
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6x^2 = +54
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x^2 = 54%2F6
x^2 = 9
x = 3 is the number
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Check solution in our initial equation
%28%282%283%29-15%29%29%2F%28%283%2B6%29%29 = 9*1%2F3 - 4
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%28%286-15%29%29%2F%28%289%29%29 = 3 - 4
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%28-9%29%2F9 = -1; confirms our solution
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How about this, did I make it understandable to you?