Systems of language equations of the form {φ(X₁, . . . , X_n) = ∅, ψ(X₁, . . . , X_n) ≠ ∅} are studied, where φ, ψ may contain set-theoretic operations and concatenation; they can be equivalently represented as strict inequalities ξ(X₁, . . . , X_n) ⊂ L₀. It is proved that the problem whether such an inequality has a solution is Σ₂-complete, the problem whether it has a unique solution is in (Σ₃ ∩ ∏₃)\ (Σ₂ ∪ ∏₂), the existence of a regular solution is a Σ₁-complete problem, while testing whether there are finitely many solutions is Σ₃-complete. The class of languages representable by their unique solutions is exactly the class of recursive sets, though a decision procedure cannot be algorithmically constructed out of an inequality, even if a proof of solution uniqueness is attached.