The Supreme Court agreed Tuesday to consider a new challenge to President Obama’s Affordable Care Act and decide whether employers with religious objections may refuse to provide their workers with mandated insurance coverage of contraceptives

The cases accepted by the court offer complex questions about religious freedom and equality for female workers along with an issue the court has not yet confronted: whether secular, for-profit corporations are protected by the Constitution or federal statute from complying with a law because of their owners’ religious beliefs.

The justices accepted two cases that produced opposite results in lower courts.

One was brought by the owners of Hobby Lobby, an arts-and-crafts chain that its owner David Green said is run on biblical principles. The full U.S. Court of Appeals for the 10th Circuit in Denver said forcing the company to comply with the contraceptive mandate would violate the Religious Freedom Restoration Act.

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