What is the proper way to check an algebraic solution?

The correct way is to plug in the answer back into the equation and see if it results in the correct solution.

Substitution is a great way to find out if the statement or equation is true and if it is both sides will be equal to the same number. Now in the case of any solution I'd just check with random numbers about 2 times. If it's no solution do the same thing. And with no solution or any solution be sure to double check your work.