The university considers race among many factors in admitting the last quarter of incoming freshmen classes. Texas fills most of the freshman class by guaranteeing admission to students who graduate in the top 10% of their Texas high school class.

Justice Anthony Kennedy said in his majority opinion that the Texas plan complied with earlier court rulings allowing colleges to take account of race in pursuit of diversity on campus. “The university has thus met its burden of showing that the admissions policy it used … was narrowly tailored,” Kennedy wrote.

The court’s three more conservative justices dissented.

The high court ruled in the case of Abigail Fisher, a white Texan who was denied admission to the university’s flagship campus in Austin in 2008. Fisher claimed she was rejected while African-American applicants with lower grades and test scores were admitted. The school said Fisher, who did not graduate in the top 10% of her high school class, would not have been admitted with or without race as a factor. But officials did conditionally offer to allow her to transfer in as a sophomore if she maintained a 3.2 grade point average at another public college in Texas.

Instead, Fisher went to Louisiana State University, from which she graduated in 2012, and pursued her lawsuit. Fisher was recruited for the suit by Edward Blum, an opponent of racial preferences who has been remarkably successful in persuading the Supreme Court to hear cases challenging the use of race in education and politics. Blum was behind a major challenge to the landmark Voting Rights Act that resulted in the court eviscerating a key provision of the law and he also led an unsuccessful challenge to states’ widespread practice of counting all their residents, not just those eligible to vote, in drawing legislative districts.

Justices heard Fisher’s case once before, and issued an inconclusive ruling in 2013 that sent her case back to a lower court and set the stage for Monday’s decision.

In 2003, the justices reaffirmed the consideration of race in the quest for diversity on campus. Their decision then set a goal of doing away with such programs in 25 years.

Texas is unique in marrying the top 10 plan to a separate admissions review in which race is one of many factors considered. The university’s current freshman class is 22% Hispanic and 4.5% African-American. White students make up less than half the school’s freshmen.

Eight states prohibit the use of race in public college admissions: Arizona, California, Florida, Michigan, Nebraska, New Hampshire, Oklahoma and Washington.