Question 588189
<pre>
            {{{abs((x+6)/(x-4))}}} = 13

We can use the principle that the absolute value of a quotient
equals the quotient of the absolute values {{{abs(A/B)}}} = {{{abs(A)/abs(B)}}}

            {{{abs(x+6)/abs(x-4)}}} = 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 = {{{29/6}}}              AND     x = {{{23/7}}}

 
Edwin</pre>