SOLUTION: How do I solve? The additive inverse of a number divided by 12 is the same as one less than 3 times its reciprocal. Find the number.

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Question 141561: How do I solve?
The additive inverse of a number divided by 12 is the same as one less than 3 times its reciprocal. 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"
Additive inverse of a number = -x
:
Just write what it says:
"The additive inverse of a number divided by 12 is the same as one less than 3 times its reciprocal."
%28-x%29%2F12 = 3%2Fx - 1
:
Multiply equation by 12x and you have:
x(-x) = 12(3) - 12x(1)
:
-x^2 = 36 - 12x
arrange as a quadratic equation on the right
0 = +x^2 - 12x + 36
This easily factors to:
(x-6)(x-6) = 0
x = +6 is the number
:
:
Check solution in the statement;
"The additive inverse of a number divided by 12 is the same as one less than 3 times its reciprocal."
%28%28-6%29%2F12%29 = 3%2F6 - 1