In this paper, we have a set of weighted linear equalities and inequalities of the form \(A_1\textbf{x}\equiv 0(\mod p), A_2\textbf{x}\not \equiv 0(\mod p)\) where all entries of \(A_1\) and \(A_2\) are in \(\{-1,0,1\}\) . The objective is to assign each \(x_{i}\) to \(\mathbb Z_p=\{0,\dots ,p-1\}\) to maximize the total weight of the satisfied equalities and inequalities. This problem is a generalization of k-Correlation Clustering problem. We design an approximation algorithm with the approximation ratio \(\max \{a,\frac{(2-p)a+p-1}{p}\}\) , where a is the weighted proportion of equalities in all equalities and inequalities. As a varies from 0 to 1, the approximation ratio varies from \(\frac{p-1}{p}\) to 1 and the minimum value is \(\frac{1}{2}\) when a is \(\frac{1}{2}\) .