The question for the justices was whether the Food and Drug Administration had acted lawfully in rejecting applications from makers of flavored liquids used in e-cigarettes.

The Supreme Court is scheduled Monday to consider the regulation of flavored e-cigarettes in a case that illustrates an enduring public health conundrum: how to keep kids away from sweet-flavored, addictive vapes while giving adult smokers better options to help them quit cigarettes.

The Supreme Court on Monday pressed the Food and Drug Administration on whether it followed the law in its effort to keep flavored e-cigarettes off shelves, weighing a lawsuit from a multibillion-dollar industry that has come under scrutiny because its products are popular with school-aged children.