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

$$\eqalign{ & {\text{4}}x = p\left( {x + 3} \right) + q\left( {x - 1} \right) \cr & \Rightarrow 4x = px + 3p + qx - q \cr & \Rightarrow 4x = \left( {p + q} \right)x + \left( {3p - q} \right) \cr & \Rightarrow p + q = 4\,and\,3p - q = 0 \cr & \Rightarrow p + q = 4\,and\,p = \frac{q}{3} \cr & \Rightarrow \frac{q}{3} + q = 4 \cr & \Rightarrow \frac{{4q}}{3} = 4 \cr & \Rightarrow q = 3 \cr & p + q = 4\,\,\,and \cr & \Rightarrow p = 1 \cr & \Rightarrow q = 3 \cr} $$