Start by looking at critical points: in this case values of x such that 2x + 7 = 0 and 6 - 3x = 0. Then you set up equation to test where the expression can be solved. For example, on -7/2 < x < 2 we would have the equation -(2x + 7) - (6 - 3x) = 8. What is x for this? That and other similar equations will give you the values of x for your equation.

-Dan

Made an oopsie! It should read (2x + 7) - (6 - 3x) = 8. Thanks to JeffM for the catch.