Supreme Court justices began to pick apart affirmative action in arguments Wednesday, looking at a case that could overhaul schools’ abilities to influence of race in the admissions process.

The 85-minute arguments for Fisher v. University of Texas centered on the school’s aim of creating a”critical mass” of minority students, with justices expressing skepticism that the college can choose what percentage of nonwhite students makes their campus diverse.

This is the first time the nation’s highest court has taken on affirmative action since 2003.

Justice Anthony Kennedy, who has been pegged as the deciding vote on this issue, hinted that some race-based admissions systems could be constitutional, though he dissented in the 2003 Grutter v. Bollinger case and has not supported affirmative action programs in the past.

The court’s decision could go several ways, deciding affirmative action is unconstitutional and striking down schools’ power to use race in admissions, deeming it is constitutional and upholding the program or ruling against only parts of the Texas school’s process, which would not impact other universities’ practices.

Because Justice Elena Kagan, who served as the Obama administration’s solicitor general, recused herself, the case could also result in a tie. A 4-4 decision would uphold the lower court’s decision in favor of the University of Texas.

The case dates back to 2007, when a white student named Abigail Fisher sued the University of Texas at Austin for denying her admission in a process that took into account her race. The University of Texas automatically accepts in-state students in the top 10 percent of their graduating class. But Fisher, who had a 3.59 GPA, did not make the cut and was evaluated in an admissions pool that takes a “holistic” approach to factors including race and socioeconomic status.