To simplify the equation \(7p + 4 = -p + 9 + 2p + 3p\), first combine the like terms on the right side of the equation.
Starting with the right side: \[ -p + 2p + 3p + 9 = (2p - p + 3p) + 9 = 4p + 9 \]
Now, the equation looks like: \[ 7p + 4 = 4p + 9 \]
Next, subtract \(4p\) from both sides: \[ 7p - 4p + 4 = 9 \] \[ 3p + 4 = 9 \]
Now, subtract \(4\) from both sides: \[ 3p = 9 - 4 \] \[ 3p = 5 \]
So, the simplified form of the equation is: \[ 3p = 5 \]
From the answer choices provided, the correct answer is: 3p = 5.