In his farewell address to the nation Tuesday night, a tearful President Obama called on Americans to keep working toward income equality, racial healing and bipartisan cooperation — the same goals he was unable to achieve over the past eight years.

With 10 days remaining in his presidency, Mr. Obama traveled to Chicago to deliver his valedictory speech to about 20,000 supporters and urge them to renew the fight for liberal values in the administration of Republican Donald Trump.

“We must forge a new social compact,” Mr. Obama said. “If we don’t create opportunity for all people, the disaffection and division that has stalled our progress will only sharpen in years to come.”

The president warned of threats facing democracy, saying race “remains a potent and often divisive force in our society.”

“If every economic issue is framed as a struggle between a hardworking white middle class and undeserving minorities, then workers of all shades will be left fighting for scraps while the wealthy withdraw further into their private enclaves,” the president said. “If we decline to invest in the children of immigrants, just because they don’t look like us, we diminish the prospects of our own children — because those brown kids will represent a larger share of America’s workforce.”

As he thanked first lady Michelle Obama, seated in the audience, the president paused to wipe away tears streaming down his face. “You made the White House a place that belongs to everybody,” he told his wife.

Mr. Obama ditched the usual setting of the White House for his last formal speech, flying his family instead to his hometown to speak to a sold-out crowd in a prime-time appearance reminiscent of a campaign rally.

As Mr. Obama walks into history, most Americans have a favorable view of him — 57 percent, according to an Associated Press-NORC Center for Public Affairs Research poll. But only 27 percent see the U.S. as more united as a result of his presidency, while 44 percent say it’s more divided.

Many Americans blame the nation’s first black president for making racial divisions worse. Two out of three Americans in the poll said Mr. Obama did not keep his promises, while 44 percent said he tried.

Mr. Obama said the speech was “my turn to say thanks” to Americans for serving as his inspiration for eight years. “You made me a better president, and you made me a better man,” he said.

The tradition of a presidential farewell address dates back to George Washington in 1796. Mr. Obama’s presidency will end at noon on Jan. 20, when Mr. Trump takes the oath of office.

The president is leaving office with much of his agenda in peril, including a repeal of Obamacare and Mr. Trump’s vow to pull out of a global climate change agreement and renegotiate the Iranian nuclear deal. Mr. Obama, who has said he could have defeated Mr. Trump in a bid for a third term, was unable to campaign effectively enough to install his chosen successor, Democrat Hillary Clinton.

When Mr. Obama mentioned the transfer of power to Mr. Trump, the audience booed until he quieted the crowd.

“I committed to President-elect Trump that my administration would ensure the smoothest possible transition, just as President Bush did for me,” he said, downplaying an increasingly hostile transition process. “It’s up to all of us to make sure our government can help us meet the many challenges we still face.”

Mr. Obama also called on Americans to overcome a deepening partisan divide.

“Democracy can buckle when we give in to fear,” he said. “So just as we, as citizens, must remain vigilant against external aggression, we must guard against a weakening of the values that make us who we are. That’s why we’ve ended torture, worked to close Gitmo, and reform our laws governing surveillance to protect privacy and civil liberties. That’s why I reject discrimination against Muslim Americans.”

He concluded his address by calling on supporters to keep working for change in the political system, and recited his campaign slogan from 2008.

“Yes we can. Yes we did. Yes we can,” he said as the crowd roared and rose to its feet.

Among his regrets are an inability to enact stiffer gun regulations and presiding over worsening partisan relations in Washington.

It’s no exaggeration to say that Republicans are counting the days until Mr. Obama leaves. House Speaker Paul D. Ryan’s office said Tuesday that Mr. Obama has been “sincere in his beliefs” but “steered our country in the wrong direction.”

“Things are about to change. The people have given us a unified Republican government, and we intend to deliver results for the American people,” the Wisconsin Republican’s office said.

Economists in general credit Mr. Obama’s policies with helping to pull the nation out of a deep recession, cutting the jobless rate along the way from 10 percent in 2009 to 4.7 percent last month.

On the international stage, critics say, America’s influence waned under Mr. Obama and Russia grew stronger.

It was the last of many speeches by Mr. Obama. In eight years, the president has given 3,575 speeches, remarks or other public comments, according to CBS White House reporter Mark Knoller, who tracks presidential records.

The round trip from Washington to Chicago and back also marked Mr. Obama’s final two flights on Air Force One, bringing his total to 1,350. Mr. Obama has flown 2,799 hours and 6 minutes on the presidential aircraft, or a total of 116 days.

Also on board was “NBC Nightly News” anchor Lester Holt, who had an interview with the president.

The president reviewed his achievements, including bringing home the vast majority of 180,000 U.S. troops from Iraq and Afghanistan, enacting Obamacare, helping pull the nation out of a deep recession, adding more than 15 million private-sector jobs, re-establishing ties with Cuba and killing Osama bin Laden.

“That’s what you did,” Mr. Obama told supporters in Chicago. “You were the change. You answered people’s hopes, and because of you, by almost every measure, America is a better, stronger place than it was when we started.”

The advocacy group Human Rights First said Mr. Obama’s administration also was good for gay citizens.

“Broadly speaking, the LGBT community accomplished three of its four major goals during the Obama administration: hate crimes legislation, open military service, and marriage equality,” the group said in a report issued Tuesday. “The final goal that remains is achieving employment nondiscrimination.”

Mr. Obama said he chose Chicago for his farewell address because the city is “where it all started.” He was elected to the U.S. Senate in 2004 while serving as an Illinois state senator representing the city; four years later, he was elected president.

The warm-up act at the indoor event at the McCormick Place convention center featured entertainer Eddie Vedder and a 24-member children’s choir. In the audience were dozens of current and former staffers, plus Vice President Joseph R. Biden and members of their families.

For Obama supporters, the address served as an emotional and historic bookend to the victory speech he gave on election night in November 2008 to about 240,000 raucous people in Grant Park.

The Obamas still have a home in the city’s Kenwood neighborhood, and the Barack Obama Presidential Center will be built in Jackson Park on the city’s south side. But for the next two years, the Obamas will live primarily in a rented house in Washington while their younger daughter, Sasha, completes high school.

The president has chafed for more than a year at Mr. Trump’s campaign slogan, “Make America Great Again.” In a Facebook post on Tuesday, Mr. Obama said his administration “made America a better, stronger place for the generations that will follow.”

“We’ve reaffirmed the belief that we can make a difference with our own hands, in our own time,” he wrote. “That’s the imperative of citizenship — the idea that, with hard work, and a generous heart toward our fellow Americans, people who love their country can change it.”

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