Inquiry-based mathematics education (IBME) includes features such as: (a) Using tasks with authentic problem contexts, (b) building on students’ everyday resources, (c) relying on small-group and whole-class discussions, and (d) establishing certain norms of participation for the inquiry classroom community (Laursen & Rasmussen, 2019). Prior research on active learning (which includes IBME) suggests inquiry approaches are more effective than lectures in undergraduate mathematics education (Freeman et al., 2014). However, inquiry-based approaches might not yield equal benefits for students from certain marginalized groups (e.g., women in Johnson et al., 2020). One important group to consider is multilingual students whose primary language differs from the language of instruction. In this dissertation, I conducted a multi-case study analysis to explore an overarching question related to equity for multilingual students: What language demands and resources do multilingual students experience in one inquiry-oriented linear algebra (IOLA) course? Grounded in a situated sociocultural theory of learning, I constructed a framework that captures language demands and resources along three interrelated dimensions: lexico-grammatical, situational, and normative. The data collected were classroom observations of one IOLA course taught by an expert instructor, as well as semi-structured interviews with 4 multilingual students from the course. The 4 students spanned a diverse range of linguistic and cultural backgrounds (Korean, Vietnamese, Malaysian, and Latino) and comfort levels with English. The interview data was analyzed using inductive and deductive coding (Miles et al., 2019). The study's findings show that (a) authentic problem contexts use complex language, especially for multilingual students; (b) “everyday” language resources for students from the dominant community might not function as such for multilingual students; (c) an emphasis on verbal participation can obscure multilingual students’ communication resources; and (d) inquiry classrooms can induce norm tensions about communication for multilingual students when the norms of their communities outside the inquiry classroom are not explicitly considered. This study underscores the opportunity to continue improving IBME to address the language demands induced for multilingual students by incorporating instructional language resources and leveraging the students’ language resources.