SOLUTION: Finding solutions to equation |(x+6)/(x-4)| = 13. Unsure how to proceed as there is a fraction in the absolute field. Any help would be appreciated.

Algebra ->  Absolute-value -> SOLUTION: Finding solutions to equation |(x+6)/(x-4)| = 13. Unsure how to proceed as there is a fraction in the absolute field. Any help would be appreciated.      Log On


   

Question 588189: Finding solutions to equation |(x+6)/(x-4)| = 13. Unsure how to proceed as there is a fraction in the absolute field. Any help would be appreciated.
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
            abs%28%28x%2B6%29%2F%28x-4%29%29 = 13

We can use the principle that the absolute value of a quotient
equals the quotient of the absolute values abs%28A%2FB%29 = abs%28A%29%2Fabs%28B%29

            abs%28x%2B6%29%2Fabs%28x-4%29 = 13

Then we can multiply through by |x-4|,  which we can do as long as x is not 4.

          |x+6| = 13|x-4|

There are two cases:

            x+6 = 13(x-4)     AND      x+6 = -13(x-4)

Solve those and get

              x = 29%2F6              AND     x = 23%2F7

 
Edwin