SOLUTION: The additive inverse of a number divided by 12 is the same as one less than three times its reciprocal. Find the number.

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Question 192238This question is from textbook Algebra 1
: The additive inverse of a number divided by 12 is the same as one less than three times its reciprocal. Find the number. This question is from textbook Algebra 1

Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let the number be x
:
-x%2F12=3%281%2Fx%29-1
:
-x=%2836%2Fx%29-12
:
-x=%2836-12x%29%2Fx
:
x%5E2-12x%2B36=0
:
%28x-6%29%28x-6%29=0
:
x=6

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let x represent the number.

Then -x is the additive inverse.

The additive inverse divided by 12 is:

The reciprocal of the number is

Three times the reciprocal of the number is

One less than three times the reciprocal is

So, solve for x



Hint: Multiply by -x first. Then collect terms and solve the easily factorable quadratic.

John