Bot GPT 4-o mini To solve the equation \(-16 + 5n = -7(-6 + 8n) + 3\), we will first simplify the right-hand side.
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Start with the right side: \[ -7(-6 + 8n) + 3 \]
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Distribute \(-7\): \[ -7 \cdot -6 + (-7) \cdot 8n = 42 - 56n \] So the right side simplifies to: \[ 42 - 56n + 3 \]
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Combine the constants: \[ 42 + 3 = 45 \] Therefore, the equation now looks like: \[ -16 + 5n = 45 - 56n \]
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Next, we will add \(56n\) to both sides to get all the \(n\)'s on one side: \[ -16 + 5n + 56n = 45 \] This simplifies to: \[ -16 + 61n = 45 \]
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Now, add \(16\) to both sides to isolate the term with \(n\): \[ 61n = 45 + 16 \] \[ 61n = 61 \]
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Finally, divide both sides by \(61\): \[ n = \frac{61}{61} = 1 \]
The solution is: \[ \boxed{1} \]
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