How many solutions are there to this equation?

Question

-1/3x + 12 = -2/3x + 20

Answer 1

There are multiple ways to think this through, but I am not sure exactly which way you would be using in class.

One thing to do is to try solving the problem outright. If you get x = #, then there is one solution. If the x's are all eliminated and you just get a true statement such as 3 = 3, then there are an infinite number of solutions. If the x's are all eliminated and you get a false statement such as 3 = 4, then there are no solutions.

-1/3x + 12 = -2/3x + 20 Add 2/3x to both sides

1/3x + 12 = 20 Subtract 12 from both sides

1/3x = 8 Multiply each side by 3 (or divide by 1/3)

x = 24

Since we got one solution, there is one solution to the problem.