Dr. Bill inquires: Dear Plutarch: how then does 'resolve' also mean to make a decision, a commitment?

Perhaps in this sense:

After one "solves" a problem, it's a usually a good idea to "make a decision or commitment" to act on the new awareness.

To express this idea epigrammatically, you could say:

When you solve, resolve, to make a difference.

"Solve" is to "resolve" what "awareness" is to "commitment".