This study sought to provide an explanation of (n=13) university students' understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of the analysis of the data, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examines the differences in the problem-solving activities of solvers who were able to make a transition from arithmetical methods to algebraic methods in contrast to those solvers who were unable to make such a transition. Results suggest that if solvers were to make a successful transition to algebra, they needed to attain post-representational levels of reflective abstraction. In addition, it is indicated that imagery is an inherent part of the development from one level of reflective abstraction to the next. The paper includes the learning tasks. Contains 30 references. (MKR)