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. make the writing short

Answer 1

Both Spencer and Jeremiah are correct in that either operation can be the first step to solve the equation \(6x - 2 = -4x + 2\).

If Spencer adds \(4x\) to both sides, he gets: \[ 6x + 4x - 2 = 2 \] This simplifies to: \[ 10x - 2 = 2 \]

If Jeremiah subtracts \(6x\) from both sides, he obtains: \[ -2 = -4x - 6x + 2 \] This simplifies to: \[ -2 = -10x + 2 \]

Both methods will eventually lead to the correct solution for \(x\). Thus, either step is valid.