The resolution of bipolar equations with usual max-triangular norm compositions (Gödel, product and Łukasiewicz) and the standard negation have been extensively studied. Recent theoretical advances extend the algebraic framework of bipolar equations to the context of non-linear lattices, considering at the same time a general class of triangular norms, an arbitrary involutive negation and a join-irreducible element of the lattice as independent term. This paper studies the resolution of bipolar inequations within the latter algebraic setting, which leads to an alternative strategy to compute the solutions set of bipolar equations.