Let's review your solution step by step.
You began with the equation:
\[ -2(4x + 8) + 2x = -5x + 10 \]
- Distributing: You correctly distributed the \(-2\) across the terms inside the parentheses:
\[ -2 \cdot 4x - 2 \cdot 8 + 2x = -5x + 10 \] This simplifies to: \[ -8x - 16 + 2x = -5x + 10 \]
- Combining Like Terms: Next, you combined the \(x\) terms on the left side:
\[ (-8x + 2x) - 16 = -5x + 10 \] This gives you: \[ -6x - 16 = -5x + 10 \]
- Getting Constants together on one side: To isolate \(x\), we can add \(6x\) to both sides:
\[ -16 = -5x + 6x + 10 \] This simplifies to: \[ -16 = x + 10 \]
- Getting \(x\) terms together: Now, to isolate \(x\), subtract \(10\) from both sides:
\[ -16 - 10 = x \] This gives you: \[ -26 = x \]
- Final Step: You can rewrite this as: \[ x = -26 \]
Your final answer is correct: \(x = -26\).
In summary, the steps you took were mostly correct, but it seems like you mixed up some notational or arithmetic errors in the explanation. The final answer is indeed \(x = -26\). Great job!
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