12 pt for whoever answers with shown work

given the equation 5 + x - 12 = x - 7.

part a. solve the equation 5 + x - 12 = x - 7. in your final answer, be sure to state the solution and include all of your work.

part b. use the values x = -4, 0, 5 to prove your solution to the equation 5 + x - 12 = x - 7. in your final answer, include all of your calculations.