is it possible to solve an absolute value problem that isn't set equal to anything? For example the absolute value of m-8 is?

I'm not sure what you're asking, but you can expand the expression:

|m-8| = \begin{cases} m-8, & \mbox{if } m \ge 8 \\ -(m-8), & \mbox{if } m < 8 \end{cases}

let me know if you're asking something else...