If 4x = p(x + 3) + q(x - 1) is an identity, then the values of p and q are?

Answer: Option B

$$\begin{array}{rl}& \text{4}x=p\left(x+3\right)+q\left(x-1\right)\\ & \Rightarrow 4x=px+3p+qx-q\\ & \Rightarrow 4x=\left(p+q\right)x+\left(3p-q\right)\\ & \Rightarrow p+q=4and3p-q=0\\ & \Rightarrow p+q=4andp=\frac{q}{3}\\ & \Rightarrow \frac{q}{3}+q=4\\ & \Rightarrow \frac{4q}{3}=4\\ & \Rightarrow q=3\\ & p+q=4and\\ & \Rightarrow p=1\\ & \Rightarrow q=3\end{array}$$