Question 134556
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."
{{{(-x)/12}}} = {{{3/x}}} - 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:
{{{(-6)/12}}} = {{{3/6}}} - 1
{{{-1/2}}} = {{{1/2}}} - 1; confirms our solution