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.
Jeremiah is correct. The first step in solving this equation is to get all the variables on one side of the equation. By subtracting 6x from both sides, you eliminate the variable from one side of the equation.
6x - 2 = -4x + 2
Subtract 6x from both sides:
-2 = -10x + 2
If Spencer were to add 4x to both sides first, the equation would become:
6x - 2 + 4x = 2
10x - 2 = 2
This is not helpful in simplifying the equation or isolating the variable x. Therefore, Jeremiah is correct in his approach to subtract 6x from both sides as the first step.
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.
What did you include in your response? Check all that apply.
Both boys are correct.
Both methods correctly use the properties of equality and inverse operations.
Both methods isolate the variable on one side of the equals sign.
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