LAS VEGAS -- Boosted by her first debate, Hillary Rodham Clinton has launched the next phase of her presidential campaign by outlining broad, general election themes -- many to the left of where she was when she ran in 2008.

Many analysts said Clinton performed better than her four adversaries at the Democratic debate here Tuesday. She also got some unexpected help from her leading rival, Vermont Sen. Bernie Sanders, when he said the public was tired of hearing about the controversy of Clinton using private emails while serving as secretary of state. Analysts also said she didn't leave any opening for Vice President Joe Biden, who's contemplating a run, to jump into the race.

With that, Clinton launched a tour that has her appearing with key constituencies, including unions, African-Americans and Hispanics. She's emphasizing economic, education and social issues, which she believes will play well with enough Americans to win in 2016. She held events with unions and minority supporters in Nevada on Wednesday and with a "Latinos for Hillary" group in Texas on Thursday and Young Democrats clubs in New Hampshire on Friday.

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In a rally at a nature preserve in the northwest part of this city, the Democratic front-runner touched on the middle class, the 2008 recession, same-sex marriage, immigration, college tuition, abortion, climate change, campaign-finance laws, unions and the Black Lives Matter campaign. A mariachi band and a gospel choir opened the event.

Clinton's address also hit key points that triggered applause from Hispanics at the rally, including her mention of her immigrant grandfather, support for the Dream Act and a call for free community college. It came the same day an independent political action committee, which supports Clinton, released a pro-Clinton ad called "Mi Hija" (My Daughter) aimed at Hispanics.

In her speech, Clinton also hearkened back to good economic times when her husband, Bill Clinton, was president. For Democrats who supported President Barack Obama in 2008 instead of her, Clinton said Obama "doesn't get the credit he deserves" for getting the nation out of recession.

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That could be seen as her effort to shore up support with Democrats who supported Obama instead of her in 2008, such as Phil and Mary Washington of suburban Henderson, two of an estimated 2,000 at the rally.

"I really want to believe in her," said Mary Washington, who described the African-American couple as loyal Democrats and retirees. "I haven't been able to really listen to her yet -- so tonight's the night."

Though she didn't back Clinton in 2008, Washington said she now believes "it's time for a woman president."

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Phil Washington said he hadn't paid attention to the other Democrats in the race -- Sanders, ex-Maryland Gov. Martin O'Malley, ex-Rhode Island Gov. Lincoln Chafee and ex-Virginia Sen. Jim Webb -- because Clinton clearly was the best candidate.

In the speech and at the debate, Clinton underscored that she's moved to the left on some issues since she first ran -- catching up to Democratic voters and the public at large in some cases, analysts have said.

Once an opponent of same-sex marriage, she now supports it. Once sounding inclined to support the Keystone pipeline and the Trans-Pacific trade agreement, she now opposes them.

She is more vocal about gun control and billionaires -- though she pointedly defended capitalism in an exchange with Sanders, who describes himself as a Democrat-socialist.

Whereas Republicans spent much of their debates talking about cracking down on illegal immigration and building a wall along the Mexican border, Clinton voices support for the Dream Act, a proposal to allow children of immigrants living in the country illegally to apply for college aid programs.

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Invoking her immigrant grandfather, she garnered applause when she said: "We all have somebody who came to this country, and aren't we glad they did?"

Later, she added: "The Republicans are doing great damage with the insults and attacks on immigrants."

Marist College pollster Lee Miringoff said it's no surprise to see Clinton move left.

"The electorate tends to be more polarized than in '08. Republicans have moved more to the right; Democrats more to the left," Miringoff said. "And their issues are different than in '08."

Miringoff said Clinton is playing to her core supporters and reaching out to Obama Democrats by "raising the issue of losing the progress of the Obama years."

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Throughout her appearances, she repeatedly took shots at Republicans in general, saying the numerous candidates jockeying for that nomination "want to go back and do what didn't work before," referring to what she called a philosophy of "cut taxes" for the wealthy and "get out of corporations' way."

In criticizing congressional Republicans for what she said was wanting things 100 percent their way, Clinton used self-deprecating humor in referring to her own, at times troubled, marriage.

"I'm not a hundred percent with anybody," she said, pausing for effect, then continuing, "my husband understands that," drawing laughter.