The topic of inequalities is one of the fundamental subject areas for the development of mathematical knowledge. Although there is a considerable body of research focused on one-variable inequalities, studies that investigate students' performance on two-variable inequalities are scarce. With this in mind, the aim of this study is twofold: first, it provides an account of the difficulties that students face in interpreting and constructing different representations of two-variable inequalities; and second, it investigates the effectiveness of a computer-supported teaching sequence aimed at developing students' understanding of different representations of two-variable inequalities. The participants in the study were 33 elementary mathematics teacher candidates. The data were gathered via a test implemented as a pre- and post-test. The main finding of the study was that students had difficulty in establishing the link between the coordinates of the points in a solution set and the algebraic representation of a two-variable inequality. Moreover, it was found that the students were not able to correctly use and interpret the logical connectives in compound inequalities. The comparison of the pre- and post-test scores indicated that the designed instructional sequence was beneficial for supporting students in understanding the different representations of two-variable inequalities.