SOLUTION: the additve inverse of a number divided by twelve is the same as one less than three times its reciprocal.

Question 134556: the additve inverse of a number divided by twelve is the same as one less than three times its reciprocal.
Found 2 solutions by solver91311, ankor@dixie-net.com:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
if is the number, then the additive inverse is and its reciprocal is . "is the same as" means "equals"

The additive inverse of a number (), divided by 12 () is the same as (=) one less than () three times its reciprocal (). Put it all together:

Add 1 to both sides:

LCD on the left is 12, so:

Cross-multiply (numerator on the left times denominator on the right equals denominator on the left times numerator on the right)

Multiply by -1:

Trinomial is a perfect square:

Hence

Check:

Answer checks.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the additive inverse of a number divided by twelve is the same as one less than three times its reciprocal.
:
Let x = a number
then
-x = additive inverse of a number
:
Write an equation for the statement:
"the additive inverse of a number divided by twelve is the same as one less than three times its reciprocal."
= - 1
Multiply equation by 12x to get rid of the denominators, and you have:
x(-x) = 12(3) - 12x
:
-x^2 = 36 - 12x
:
Arrange as a quadratic equation:
x^2 - 12x + 36 = 0
Factors to
(x-6)^2 = 0
x = +6
:
Check solution in original equation:
= - 1
= - 1; confirms our solution
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