Question

In the equation 6x – 2 = –4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain.

Answer 1

Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.

Answer 2

If you would like to know who is correct, you can find this using the following step:

6x - 2 = -4x + 2

Spencer:
6x - 2 = -4x + 2 /+4x
6x - 2 + 4x = -4x + 2 + 4x
10x - 2 = 2

Jeremiah:
6x - 2 = -4x + 2 /-6x
6x - 2 - 6x = -4x + 2 - 6x
-2 = -10x + 2

They both are correct. But in Jeremiah's version of solving the equation, we would have to multiply equation by -1 (or add 10x to both sides), which we don't have to do in the Spencer's version.