To solve the equation \(-9 + 2(n + 3) = 4n - 7\), we will first simplify and combine like terms.
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Start with the original equation: \[ -9 + 2(n + 3) = 4n - 7 \]
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Distribute \(2\) on the left side: \[ -9 + 2n + 6 = 4n - 7 \]
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Combine like terms on the left side: \[ (2n - 3) = 4n - 7 \]
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Next, we want to isolate \(n\). Let's move \(2n\) to the right side by subtracting \(2n\) from both sides: \[ -3 = 4n - 2n - 7 \] \[ -3 = 2n - 7 \]
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Now, add \(7\) to both sides: \[ -3 + 7 = 2n \] \[ 4 = 2n \]
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Finally, divide both sides by \(2\): \[ n = 2 \]
Thus, the solution to the equation is: \[ \boxed{2} \]