Let H be a complex Hilbert space and A be a non-zero positive bounded linear operator on H. The main aim of this paper is to discuss a general method to develop A-operator seminorm and A-numerical radius inequalities of semi-Hilbertian space operators using the existing corresponding inequalities of bounded linear operators on H. Among many other inequalities we prove that if S, T, X ∈ BA (H), i.e., if A-adjoint of S, T, X exist, then 2∥S ]A XT∥A ≤ ∥SS]A X + XT T]A ∥A. Further, we prove that if T ∈ BA(H), then 1 4 ∥T ]A T + T T]A ∥A ≤ 1 8 ∥T + T ]A ∥ 2 A + ∥T – T ]A ∥ 2 A ≤ 1 8 ∥T + T ]A ∥ 2 A + ∥T – T ]A ∥ 2 A + 1 8 c 2 A.