I think there are shades of correctness to your answer (at the upper echelons of math study, as it were, there will be no answer book for you to check), but the

I think there are shades of correctness to your answer (at the upper echelons of math study, as it were, there will be no answer book for you to check), but the act of confirming your answers should be transitioned in and taught; which from this author's perspective hasn't happened. Further, there should be education, refinement, and strengthening of learning to validate one's own answers before leaving them to flounder in a 200 level STEM-focused course. (Honestly, I'd probably have a better relationship with math if it were taught to me in the method you seem to require as "actual math".)