Former Vice President Joe Biden returned to the campaign trail on Friday after a Democratic debate that largely reinforced his front-runner status for the party's presidential nomination, leaving his rivals searching for how to wrest away the top spot.

The candidates who participated in Thursday night's debate in Houston, and those scrambling to try to qualify for next month's debate in Ohio, have less than five months to plead their case to voters before the first nominating contest in Iowa on February 3, 2020.

Fire on different policy proposals

Biden on Friday held campaign events in Houston, where a day earlier he clashed with liberal rivals Elizabeth Warren and Bernie Sanders on healthcare, challenging the two U.S. senators to be honest about the cost of their plans.

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Five takeaways as outsiders shine in Democratic debate

Biden came under fire from former U.S. Housing Secretary Julian Castro, who incorrectly accused the former vice president of forgetting what he had just in an exchange seen as an attack on Biden's age. And Biden's comments about racial inequality in schools prompted a rebuke from rival U.S. Senator Cory Booker.

"We are at a tough point right now, because there's a lot of people concerned about Joe Biden's ability to carry the ball all the way across the end line without fumbling,” Booker said on CNN after the debate.

After meeting students at historically black Texas State University in Houston on Friday – where the debate was held – Biden was asked about the barbs from Castro and Booker aimed at his age.

He said Castro had gotten his facts wrong. Asked to respond to Booker, Biden said he will “carry the ball over the finishing line.”

But the top 10 Democratic candidates, sharing the debate stage for the first time after the party toughened the rules to qualify, also stressed their shared opposition to Republican President Donald Trump and scaled down some of the bickering that marked the first two debates this summer.

Biden was sharper and more aggressive than in the earlier matchups, leaving him in a strong position as his rivals evaluate the best strategy in the race to pick a Democratic challenger to Trump in the November 2020 election.

Aside from Biden, Sanders and Warren, none of the other 17 Democratic contenders is regularly hitting double digits in support in opinion polls.

Several major events are on the campaign schedule in coming weeks. Biden, Sanders and at least three other candidates are expected on Monday to attend the Galivants Ferry Stump meeting in South Carolina.

Also the Democratic National Committee announced on Friday the next debate will be held in Westerville, Ohio, on October 15 and possibly October 16 depending on the number of qualifying candidates.

At least one more candidate, billionaire activist Tom Steyer, has met the tougher qualifications for the next debate.

Castro on the offensive

Castro led the charge on Thursday against Biden by accusing him of flip-flopping in his description of his own healthcare proposal, which left a chance to the public to keep their private insurances if they want to.

"Are you forgetting what you said two minutes ago?" Castro, 44, asked Biden, 76, who has faced questions about his age.

Later, he accused Biden of being quick to tie himself to former President Barack Obama when it suited him and walk away when it did not. Biden was Obama's vice president for eight years.

Biden, who served under the first black U.S. president and enjoys strong support from likely black primary voters, also drew criticism for his response to whether Americans had a duty to repair slavery's legacy.

He transitioned into an answer related to education that suggested bringing social workers into black families' homes to "help them deal with how to raise their children" and having a "record player on at night" to help with language acquisition.

Booker said on CNN after the debate that Biden is sometimes "meandering in his speech."

"He's talking about people in communities like mine listening to record players .... There are definitely moments when you listen to Joe Biden and you just wonder," Booker said.

Biden reiterated his response while speaking to reporters in Houston on Thursday after meeting students at Texas State. He said investment in early education is important for all children, "particularly people of color from poorer backgrounds." Often parents "need to have some help, they need to be encouraged," the former vice president said.

Racial disparities

Told by one reporter that some have criticized him for his debate response, given that he is white, Biden said that it was important to talk about racial disparities in education. "I have done it my whole life. That's why I have such overwhelming support from the African-American community," he said.

Antjuan Seawright, a Democratic strategist in South Carolina, which hosts the fourth nominating contest next year and the first that will have a sizable proportion of black voters, said he did not think Biden's remarks would hurt him. Black voters have a "genuine love and affection" for Biden, Seawright said, and his decades-long political career speaks for itself.

"They know who he is, there's no second-guessing his record," he said.

Most candidates avoided the attacks that marked the first two rounds of the debates. Those exchanges had dismayed some Democrats, who urged the candidates to focus on laying out their own positive agendas.

(With input from Reuters)