Solving Equations with Variables on Both Sides

The Good...

x + 4 = 2x - 6

the Bad...

4(1 - x) + 3x = -2(x - 1)

and the Ugly...

(-6a - 2)4 = 16a  

... not to mention the Downright Nasty!

(¹/₄)(12x + 16) = 10 - 3(x - 2)

General Strategy

a) SIMPLIFY FIRST !!

     - Distribute
     - Combine Like Terms
     - When you have a Fractional Coefficent
          - If possible, Distribute      or....
          - FRAC-ATTACK! using the reciprocal

b) Collect like variables to the same side using addition or subtraction

c) Solver's Choice:

     1) Collect variables to the left side always
     2) Collect variables to the side with the greater coefficient (avoids negative coefficients)
     3) Best of Both Worlds!!  Collect the variables to the side with the greater coefficient, then switch sides if necessary.