Over more than three hours of oral arguments on Tuesday, justices grappled with questions about sex and gender as the Supreme Court heard cases on whether bans in Idaho and West Virginia are violating transgender athletes’ rights to compete in organized sports.

Attorneys for Lambda Legal and the American Civil Liberties Union argued the states violated the constitutional rights of Becky Pepper-Jackson, 15, and Lindsay Hecox, 25, when they barred them from competing. Attorneys for Idaho and West Virginia claimed it was impossible for states to sort through which trans people should and should not qualify for athletics and therefore that the states needed a blanket ban against all transgender women.

The cases, Little v. Hecox and West Virginia v. B.P.J could have big implications for transgender athletes and trans people more broadly — but rulings could just as likely be limited to the two athletes who defy conservative stereotypes about transgender athletes.