The U.S. Supreme Court today takes up one of the most important abortion cases in decades, the first high-profile issue to be heard since Antonin Scalia’s death left the court with eight justices.

“The most momentous abortion case in a quarter century is thrown into turmoil by the prospect that the court won’t be able to give an answer because it will end in a tie,” says Tom Goldstein, publisher of the SCOTUSblog website and a lawyer who appears before the Supreme Court.

Abortion clinics and doctors are challenging a Texas law that could force more than three-quarters of the state’s clinics to shut down.

Passed in 2013, it imposes two requirements. Clinics providing abortion services must meet the same building standards as ambulatory surgical centers. And doctors providing abortion services must have admitting privileges at nearby hospitals.

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The court’s decision will affect similar laws in 12 other states. Some are now on hold because of court challenges. Just last week, a federal appeals court upheld a Louisiana law requiring abortion doctors to have hospital admitting privileges.

“The Texas law is an absolute sham,” says Nancy Northup of the Center for Reproductive Rights, whose lawyers will argue the case for the challengers.

They say abortion patients rarely require hospitalization, and many patients simply take two pills.

“Abortion is one of the safest and most common procedures in contemporary medicine,” says the court brief for the challengers.

Surgical patients undergo “a 10-minute procedure, without general anesthesia, in the outpatient setting of a doctor’s office or clinic. Complications from abortion are extremely rare.”

The requirements of the Texas law, the challengers say, will make abortion services more expensive without improving their safety.

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Since the law was passed, the number of clinics providing abortion services in Texas dropped to 19 from 42. That number could fall to 10 if the Supreme Court upholds the law.

Texas defends the restrictions, arguing that states have wide discretion to pass laws in areas where there is medical and scientific uncertainty. The state says the law was passed “to ensure patient safety and raise standards of care.”

If the Supreme Court upholds the law, the state says, at least one abortion clinic would remain open in every metro area that currently has one. More than 90 percent of women of reproductive age live within 150 miles of one of those clinics, the state’s lawyers say.

A key question for the Supreme Court is how much leeway states have to impose restrictions on abortion. Texas says the courts should give legislatures latitude when medical opinion is divided.

But the challengers say the courts must evaluate whether the restrictions would actually make abortions safer, rather than simply deferring to the states.

The restrictions in Texas, Louisiana, and a dozen other states represent a new front in efforts to restrict abortion. They focus on protecting the health and safety of the mother rather than the life of the fetus.

At the heart of the case is the standard for assessing abortion limits that was first announced by the Supreme Court in 1992. State laws cannot create “undue burden” on a woman’s constitutional right to terminate her pregnancy before the fetus attains viability.

A law imposes such a burden, the court said in the case of Planned Parenthood v Casey, if its “purpose or effect is to place substantial obstacles in the path” of a woman seeking to exercise that right.

While an eight-member court raises the prospect of a tie, opponents of the Texas law have some reason for optimism. Last June, after a federal appeals court upheld the Texas law, the Supreme Court blocked most of it from going into effect while the justices considered whether to take up the case.

That action required the votes of five justices, the same number the challengers would need to prevail.

Justice Scalia consistently voted in favor of abortion restrictions.

A decision is expected by the end of June.

This story first appeared on NBCNews.com.