Solve: \( \frac{2 n-7}{-7}=\frac{n-1}{2} \). Enter a fraction if needed. Provide your answer below: \( n=\square \)
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To solve the equation \( \frac{2n-7}{-7}=\frac{n-1}{2} \), we can start by cross-multiplying to eliminate the fractions. Cross multiplying gives us: \[ 2(2n - 7) = -7(n - 1) \] Distributing on both sides: \[ 4n - 14 = -7n + 7 \] Now, let's get all the \( n \) terms on one side by adding \( 7n \) to both sides: \[ 4n + 7n - 14 = 7 \] \[ 11n - 14 = 7 \] Next, add 14 to both sides: \[ 11n = 21 \] Now, divide by 11: \[ n = \frac{21}{11} \] So, the answer is: \( n=\frac{21}{11} \)