Solve for \( p \) \( \frac{s p-2}{3}+\frac{p}{2}=8 \)

To solve for \( p \) in the equation \( \frac{s p - 2}{3} + \frac{p}{2} = 8 \), we can start by eliminating the fractions. Multiply the entire equation by the least common multiple (LCM) of the denominators, which is 6 in this case: \[ 6 \left( \frac{s p - 2}{3} \right) + 6 \left( \frac{p}{2} \right) = 6 \cdot 8 \] This simplifies to: \[ 2(s p - 2) + 3p = 48 \] Expanding this gives: \[ 2s p - 4 + 3p = 48 \] Now, combine like terms: \[ 2s p + 3p - 4 = 48 \] Adding 4 to both sides results in: \[ 2s p + 3p = 52 \] Factoring out \( p \) yields: \[ p(2s + 3) = 52 \] Finally, divide both sides by \( 2s + 3 \) to isolate \( p \): \[ p = \frac{52}{2s + 3} \] So the solution for \( p \) is: \[ p = \frac{52}{2s + 3} \]