Let's go through your work step by step and check for any errors.
You started with the equation: \[ -2(4x+8)+2x = -5x + 10 \]
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Distribute: You correctly distributed: \[ -2(4x) - 2(8) + 2x = -5x + 10 \] This simplifies to: \[ -8x - 16 + 2x = -5x + 10 \]
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Combine Like Terms: You combined the \( -8x \) and \( 2x \): \[ -8x + 2x - 16 = -5x + 10 \] This simplifies to: \[ -6x - 16 = -5x + 10 \] So this step is correct.
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Get constants together on one side: From here, let's isolate the variable terms on one side. You want to add \( 5x \) to both sides: \[ -6x + 5x - 16 = 10 \] This simplifies to: \[ -1x - 16 = 10 \]
Now, we will add 16 to both sides to isolate the x-term: \[ -x = 10 + 16 \] \[ -x = 26 \] When you multiply both sides by -1: \[ x = -26 \]
- Get x-terms together on one side: You stated: \[ -16 = x + 10 \] This step appears to be incorrect through the process, and it leads to confusion. Let's clarify it.
Your final solution should state: \[ x = -26 \]
So overall, your steps were logical, but there were mistakes in how you derived your solutions. The correct final answer is \( x = -26 \).
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