Forces and equilibrium — practice question

Two particles $P$ and $Q$, whose masses are $0.4\ \text{kg}$ and $0.7\ \text{kg}$ respectively, are joined to the two ends of a light inextensible string. This string runs over a fixed smooth pulley attached to the edge of a rough plane. The coefficient of friction between $P$ and the plane is $0.5$. The plane is inclined at an angle $\alpha$ to the horizontal, with $\tan \alpha = \frac{3}{4}$. Particle $P$ is on the plane and particle $Q$ is suspended vertically. The section of string from $P$ to the pulley is parallel to a line of greatest slope of the plane (see diagram). A force of magnitude $X\ \text{N}$, acting directly down the plane, is applied to $P$.