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

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) (Show Source): You can put this solution on YOUR website!
Let x = "a number"
:
Break it down, write an expression for each phrase
:
If fifteen less than two times a number
2x - 15
:
"is divided by six more than the number,"

:
The word "is" usually mean "=" in these type problems
"result is four less than 9 times the reciprocal of that number.
= 9* - 4
Or
= - 4
:
Find the number
Multiply equation by x(x+6) to get rid of the denominators
x(x+6)* = x(x+6)* - x(x+6)(4)
:
Cancel the denominators and you have:
x(2x-15) = 9(x+6) - 4(x^2 + 6x)
:
2x^2 - 15x = 9x + 54 - 4x^2 - 24x
:
Arrange as a quadratic on the left:
2x^2 + 4x^2 - 15x - 9x + 24x - 54 = 0
:
6x^2 - 54 = 0
:
6x^2 = +54
:
x^2 =
x^2 = 9
x = 3 is the number
:
:
Check solution in our initial equation
= 9* - 4
:
= 3 - 4
:
= -1; confirms our solution
:
:
How about this, did I make it understandable to you?
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