1. The problem asks to find the value of $p$ that satisfies the equation $4p - 5p = 14$. 2. Combine like terms on the left side: $4p - 5p = (4 - 5)p = -1p = -p$. 3. So the equation simplifies to $-p = 14$. 4. To solve for $p$, divide both sides by $-1$: $$p = \frac{14}{\cancel{-1}} \times \cancel{-1} = -14$$ 5. Therefore, the solution is $p = -14$. 6. Checking the options, the correct answer is a. -14.