Solve for \( p \) \( \frac{4 \mathrm{p}+2}{3}-5=1 \) \( \mathrm{p}=[?] \)

To solve for \( p \), we start with the equation: \[ \frac{4p + 2}{3} - 5 = 1 \] First, let's isolate the fraction by adding 5 to both sides: \[ \frac{4p + 2}{3} = 1 + 5 \] This simplifies to: \[ \frac{4p + 2}{3} = 6 \] Next, we eliminate the fraction by multiplying both sides by 3: \[ 4p + 2 = 18 \] Now, we subtract 2 from both sides: \[ 4p = 16 \] Finally, we divide by 4: \[ p = 4 \] Thus, the solution is: \[ p = 4 \]