How to project a 3D point onto a plane along another (axis) vector?
You can determine x by calculating line-plane intersection. Your line starts at P and has direction D=[1, 0, 0], and plane T=[V, N]. This can be done as follows:
$$x=\frac{(V-P)\cdot N}{N\cdot D}$$
x is the distance from P along D to the intersection point with T (assuming both D and N are unit vectors)