The country’s highest court does not say why it agrees to hear specific cases, but legal analysts say that this case combines hot-button issues in one question: abortion rights and free speech, and a state’s responsibility to balance the two.

“That’s the issue the court will be looking at, and obviously [the state’s] argument is, ‘we’re trying to limit as little speech as possible by homing in on a problem,’ ” said Martha F. Davis, a professor at Northeastern University School of Law who has advocated in support of similar buffer zone laws.

She added, “Here in Boston, it’s not an academic issue . . . You have a situation where there has been violence, and this has put an end to that.”

The law, which prohibits any type of demonstration for or against abortion within a 35-foot zone around driveways and entrances of abortion clinics, had been unsuccessfully challenged in federal court in Massachusetts several times. A federal appeals court in California struck down parts of a similar law there in 2011, however, finding that the law was not neutral because police officers were one-sided in their enforcement, citing protesters but not people who were defending the patients.