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