<p>This study investigates pre-service and in-service mathematics teachers’ ways of reasoning on the solution set of a system of compound linear inequalities. Using the qualitative case study method, we explored pre-service and in-service teachers as two cases focusing on their solution approaches and reasoning about the solution set for a specific task. Individual written solutions to the task and task-based interviews conducted with purposefully selected participants were the data sources. The results indicated an overreliance on the algorithmic methods of equations while solving the system of compound linear inequalities. The chi-square test showed no statistically significant difference in solution preferences between teacher groups, regardless of their professional status. The most notable finding was that participants in both groups showed a lack of preference for the graphical approach. The interviewed participants started to think about the meaning of the solution set as a shaded area just after transforming algebraic inequalities to the graphical register. We conjectured pre-service and in-service teachers’ genuine understanding of the solution set of the system of linear compound inequalities is directly related to their ability to use transformations between or within representational registers. Based on the findings, we also made some inferences on the general issues about the teaching and learning of inequalities.</p>