Solve for \( p \) \( \frac{5 p-2}{3}+\frac{p}{2}=8 \)

To solve for \( p \) in the equation \( \frac{5 p-2}{3}+\frac{p}{2}=8 \), let's first eliminate the fractions by finding a common denominator. The common denominator of 3 and 2 is 6. Multiply every term by 6: \[ 6 \cdot \left(\frac{5p-2}{3}\right) + 6 \cdot \left(\frac{p}{2}\right) = 6 \cdot 8 \] This simplifies to: \[ 2(5p - 2) + 3p = 48 \] Expanding the equation gives: \[ 10p - 4 + 3p = 48 \] Combine like terms: \[ 13p - 4 = 48 \] To isolate \( p \), add 4 to both sides: \[ 13p = 52 \] Finally, divide by 13: \[ p = 4 \] Thus, the solution is \( p = 4 \).