Question 114531
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,"
{{{((2x-15))/((x+6))}}}
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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.
{{{((2x-15))/((x+6))}}} = 9*{{{1/x}}} - 4
Or
{{{((2x-15))/((x+6))}}} = {{{9/x}}} - 4
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 Find the number
Multiply equation by x(x+6) to get rid of the denominators
x(x+6)*{{{((2x-15))/((x+6))}}} = x(x+6)*{{{9/x}}} - 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 = {{{54/6}}}
x^2 = 9
x = 3 is the number
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Check solution in our initial equation
{{{((2(3)-15))/((3+6))}}} = 9*{{{1/3}}} - 4
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{{{((6-15))/((9))}}} = 3 - 4
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{{{(-9)/9}}} = -1; confirms our solution
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How about this, did I make it understandable to you?