We give a polynomial time algorithm that solves a CSP over 𝐙 with linear inequalities of the form c^{a₁} x - c^{a₂} y ≤ b where x and y are variables, a₁, a₂ and b are parameters, and c is a fixed constant. This is a step in classifying the complexity of CSP(Γ) for first-order reducts Γ from (𝐙, < ,+,1). The algorithm works by first reducing the infinite domain to a finite domain by inferring an upper bound on the size of the smallest solution, then repeatedly merging consecutive constraints into new constraints, and finally solving the problem using arc consistency.