We tackle the problem of computing counterfactual explanations -- minimal changes to the features that flip an undesirable model prediction. We propose a solution to this question for linear Support Vector Machine (SVMs) models. Moreover, we introduce a way to account for weighted actions that allow for more changes in certain features than others. In particular, we show how to find counterfactual explanations with the purpose of increasing model interpretability. These explanations are valid, change only actionable features, are close to the data distribution, sparse, and take into account correlations between features. We cast this as a mixed integer programming optimization problem. Additionally, we introduce two novel scale-invariant cost functions for assessing the quality of counterfactual explanations and use them to evaluate the quality of our approach with a real medical dataset. Finally, we build a support vector machine model to predict whether law students will pass the Bar exam using protected features, and used our algorithms to uncover the inherent biases of the SVM.