Solutal convection has a significant effect on the transport of impurity in porous media. Such transport processes can observe in various geophysical systems. Solutal convection is often considered by analogy with thermogravitational convection in porous media. Usually, the fact that an impurity can interact with the solid matrix of media is not taken into account. The most popular approach that allows taking this fact into account is the MIM (mobile-immobile media). The present article is devoted to investigation the excitation of solutal convection in an inclined elongated rectangular domain filled with a porous medium, in a gravity field at a constant longitudinal pressure and concentration drops. The Darcy-Boussinesq law is used as a filtration model. The problem is solved analytically by method of solution expansion by a series of small parameter within weak buoyancy approximation. Analytical expressions for the concentration and pressure fields are obtained for the state without gravity. The reduced equations for the small gravity effect in comparison with base flow effect produced by pressure drop are derived. It is shown that solution consists of two separated parts. The first one is independent on transversal coordinate and describes the effect of inclination. The second part depends on transversal coordinate and presents the convective motion. It is shown that the non-convective case is unstable at any small concentration difference in the present of gravity force, and the resulting flow is a solitary convective cell with low intensity. The inclination speeds up the fluid flow and impurity transport, its effect is much greater than convective motion.