x+2/2(x-2)= 2/3

Question

If the numerator is 1/2 of the Denominatore... Add two to the Numerator and minus 2 from the Denominator. The answer should be equivalent to 2/3

Answer 1

How you have the equation set up is a bit unclear, but I'm assuming it looks like the following:

       (x+2) / 2(x-2) = 2/3

Here, we have an unknown variable, x, which we are looking to solve for.

First, distribute the 2 in the denominator of the fraction on the left hand side of the equation:

        (x + 2) / (2·x - 2·2) = 2/3

        (x + 2) / (2x - 4) = 2/3

Now we can cross multiply:

        3·(x + 2) = 2·(2x - 4)

        3·x + 3·2 = 2·2x - 2·4

           3x + 6 = 4x - 8 

Move all terms with the variable x to one side of the equation and all other terms to the other side, then combine like terms and solve for x:

           3x + 6 = 4x - 8

         - 3x           - 3x

     ____________________

            0 + 6  =  1x - 8         ==>         6 = x - 8

                                                        + 8       + 8

                                                     ________________

                                                          14 = x