SOLUTION: The additive inverse of a number divided by 16 is the same as 1 less than -5 times its reciprocal. Find the number.

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Question 189277: The additive inverse of a number divided by 16 is the same as 1 less than -5 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!
The additive inverse of a number divided by 16 is the same as 1 less than -5 times its reciprocal.
Find the number.
:
Let x = "a number"
%28-x%29%2F16 = -5(1%2Fx) - 1
%28-x%29%2F16 = -5%2Fx - 1
multiply equation by -1, get rid of all these negatives:
x%2F16 = 5%2Fx + 1
Multiply equation by 16x, results:
x^2 = 16(5) + 16x
:
x^2 = 80 + 16x
:
x^2 -16x - 80 = 0
Factors to:
(x-20)(x+4) = 0
:
x = +20
x = -4
:
:
Check solutions in original equation:
x=20
%28-20%29%2F16 = -5(1%2F20) - 1
-1.25 = -.25 - 1
and
x=-4
%28-%28-4%29%29%2F16 = -5(1%2F%28-4%29) - 1
+.25 = +1.25 - 1