75 points
answer the following questions

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.

given the equation 5 + x - 14 = x - 7.

part a. solve the equation 5 + x - 14 = x - 7. in your final answer, be sure to state the solution and include all of your work.

part b. use the values x = -2, 0, 3 to prove your solution to the equation 5 + x - 14 = x - 7 . in your final answer, include all of your calculations.

given the equation 5 + x -12 = 2x - 7.

part a. solve the equation 5 + x - 12 = 2x - 7. in your final answer, be sure to state the solution and include all of your work.

part b. use the values x = -0.5,0,1 to prove your solution to the equation 5 + x - 12 = 2x - 7 . in your final answer, include all of your calculations.

given the equation 5 + x -12 = 2x - 7.

part a. solve the equation 5 + x - 12 = 2x - 7. in your final answer, be sure to state the solution and include all of your work.

part b. use the values x = -0.5,0,1 to prove your solution to the equation 5 + x - 12 = 2x - 7 . in your final answer, include all of your calculations.

create a single variable linear equation that has no solution. solve the equation algebraically to prove that it does not have a solution.
create a single variable linear equation that has one solution. solve the equation algebraically to prove that there is one distinct solution for the equation.
create a single variable linear equation that has infinitely many solutions. solve the equation algebraically to prove that there is an infinite number of solutions for the equation