Let λ1, λ2 be positive real numbers such that $${\frac{{\lambda_1}}{{\lambda_2}}}$$ is irrational and algebraic. For any (C, c) well-spaced sequence $${\mathcal {V} = \{{v_i}\}_{i = 1}^\infty}$$ and δ > 0 let $${E( {\mathcal {V},X,\delta})}$$ denote the number of elements $${v \in \mathcal {V}, v \le X}$$ for which the inequality $$| {\lambda_1 p_1 + \lambda_2 p_2 - v} | < X^{- \delta}$$ is not solvable in primes p 1, p 2. In this paper it is proved that $$E( {\mathcal {V},X,\delta}) \ll X^{\frac{4}{5} + \delta + \varepsilon}$$ for any $${\varepsilon > 0}$$ . This result constitutes an improvement upon that of Brüdern, Cook, and Perelli for the range $${\frac{2}{{15}} < \delta < \frac{1}{5}}$$ .