Explicit formulae for the K−functional for the general couple ((A0, A1)Φ0, (A0, A1)Φ1), where (A0, A1) is a compatible couple of quasi-normed spaces, are proved. As a consequence, the corresponding reiteration theorems are derived. Optimal embeddings are proved for generalized inhomogeneous Sobolev spaces W kE, built-up over quasi-normed rearrangement invariant spaces E that are intermediate for the couple (L1, L∞) on Rn, 1 ≤ k < n, into quasi-normed rearrangement invariant spaces G. Both subcritical and critical cases are investigated and optimal spaces E, G are constructed and characterized.