Hillary Clinton took a giant step toward clinching her party’s presidential nomination Tuesday night, completely dominating the South with big wins in the Florida and North Carolina primaries and proving she can win in the Midwestern heartland with victories in Ohio and Illinois over Democratic rival Sen. Bernard Sanders.

With her win in Ohio and Illinois and a strong showing in Missouri, Mrs. Clinton abruptly halted all the momentum Mr. Sanders had built up with his surprise win in Michigan last week, and she is quickly closing off all of the Vermont senator’s potential pathways to the Democratic nomination.

The former secretary of state’s already massive lead in the all-important delegate race will grow after her string of wins, and she told her supporters Tuesday night that the nomination is within sight as she increasingly turns her focus toward November’s general election. She made the case again Tuesday night that she has the right experience to be president and can actually deliver for the American people once in the Oval Office, and she took veiled shots at Mr. Sanders‘ ambitious, expensive proposals.

“We are moving closer to securing the Democratic Party nomination and winning this election in November,” she told supporters in West Palm Beach, Florida. “Every candidate makes promises but every candidate owes it to you to be clear and direct about what our plans will cost and how we’re going to make them work. That’s the difference between running for president and being president.”

Speaking to his supporters Tuesday night in Arizona, Mr. Sanders hinted that he’s content with losing the race to Mrs. Clinton as long as his campaign’s relentless focus on Wall Street reform and income inequality have an impact on the party’s larger agenda.

“If you want to vote for me, great. If you don’t, that’s OK,” he said. “But what I do not want to see is billionaires spending unlimited sums of money buying elections and undermining the democracy which has made our country so great.”

In North Carolina, with about 92 percent of the vote in, Mrs. Clinton led Mr. Sanders 54.6 percent to 40.7 percent. In Florida, with more than 98 percent of precincts in, Mrs. Clinton had 64.5 percent to 33.3 percent for Mr. Sanders.

In Ohio, Mrs. Clinton pulled out a decisive win. With 91 percent of the vote in, Mrs. Clinton had 56.5 percent to 42.7 percent for Mr. Sanders.

With 94 percent of the precincts reporting in Illinois, Mrs. Clinton was beating rival Mr. Sanders 50.6 percent to 48.6 percent and was projected as the winner by CNN.

The primary in Missouri was still too close to call as of 12:30 a.m.

In her victory speech, Mrs. Clinton said the next president must not “embarrass” this country, a clear shot at GOP presidential front-runner Donald Trump, possibly previewing the November matchup.

“We should be breaking down barriers, not building walls,” she said, taking aim at Mr. Trump’s plan to build a U.S.-Mexico border wall. “Our next commander in chief has to be able to defend our country, not embarrass it; engage our allies, not alienate them.”

For Mr. Sanders, Tuesday’s defeats leave him with little in the way of a realistic path to the nomination. The senator has promised to stay in the race all the way until the Democratic Party convention in July, but the delegate math is not on his side and the momentum is now firmly with the Clinton campaign again.

Mr. Sanders has struggled to compete with Mrs. Clinton among minority voters and has been riding strong support among working-class white Democrats to victories in states such as New Hampshire, Kansas, Minnesota and Kansas.

Even with his already slim chances greatly diminished after Tuesday’s results, Mr. Sanders has given little indication he’ll give up the fight, and is given a good chance of scoring some victories in the next round of primaries through the end of the month.

But Mrs. Clinton will emerge from Tuesday’s contests having added to her substantial lead in the delegate count.

Heading into Tuesday, Mrs. Clinton led Mr. Sanders among pledged delegates — those awarded as a result of actual voting — by 214. Including superdelegates, the party officials who are free to support whomever they choose, Mrs. Clinton’s lead is much greater, 1,235 to 580.

About 691 delegates were at stake in Tuesday’s contests, though Democratic Party rules award delegates proportionally.

Because of her convincing wins in Florida, North Carolina and Ohio and her narrow victory in Illinois, Mrs. Clinton will increase her lead over Mr. Sanders significantly.

Mr. Sanders‘ supporters, however, believe the senator will stick to his pledge to fight on all the way to the convention.

“Don’t count us out. We’re a long way from naming our nominee,” said Eva Brandt, who voted for Mr. Sanders Tuesday in Palm Beach, Florida.

Electability concerns

While Mrs. Clinton again trailed badly among young voters, she seems to be picking up at least some voters who identify with Mr. Sanders ideologically but doubt the senator’s ability to actually win a general election in November.

“I love Bernie and he’s been raising a lot of important issues, but he’s just not electable,” said Len Barrack, a Jupiter, Florida, resident who cast his ballot for Mrs. Clinton. “In primaries, both parties get pulled further to the left and further to the right. Once we get into the general, we’ll see both sides move more toward the center.”

Some voters even go so far as to say they believe Mr. Sanders has a better platform and is a more authentic candidate, but they still voted for Mrs. Clinton.

“I’m more liberal, so I love what Bernie stands for and is about — he’s more authentic,” said Deborah Owen, 64, of Palm Beach Gardens, Florida. “But I want someone who is going to win and continue [President] Obama’s issues, and that’s Hillary.”

But Tuesday’s results also highlight a number of ongoing challenges for Mrs. Clinton, not the least of which is her inability to inspire voters in the way Mr. Sanders has. Not only is she faring poorly among young voters, she also continues to do poorly among voters who say they’re looking for a new direction or more liberal policies.

Mrs. Clinton consistently does well among those who want the next president to continue President Obama’s policies, exit polls show, but Mr. Sanders leads among those who want the next Democratic president to go even further.

Joe Chuk, 62, a retired steel mill worker in Struthers, said the way in which Mr. Sanders has inspired young Democrats with his progressive message is striking.

“Let these young people have who they want,” he said. “Right now I’m voting for Bernie Sanders, and not that I wouldn’t vote for Hillary in the end, but I guess I’d just say I’m looking for different blood.”

The battle in the Midwest between Mr. Sanders and Mrs. Clinton had turned nasty over the past several weeks as the former first lady sought to recover from her shock defeat last week in Michigan.

Leading up to Tuesday, Mrs. Clinton and Mr. Sanders had battled over manufacturing, trade and the federal government’s bailout of the auto industry. The Sanders campaign had launched a prolonged assault highlighting Mrs. Clinton’s support of trade deals such as NAFTA, which Mr. Sanders argues did irreparable harm to states such as Ohio and Illinois. Mr. Sanders even dubbed Mrs. Clinton the “outsourcer in chief.”

Mrs. Clinton, meanwhile, rolled out her own Midwestern strategy: paint Mr. Sanders as an opponent of the bailout package that saved the U.S. auto industry.

Ahead of the Midwest voting, Mrs. Clinton also had to walk back her promise to “put a lot of coal miners and coal companies out of business,” which threatened to turn off voters in coal-dependent Missouri, Ohio and Illinois.

Mrs. Clinton made the comment Sunday on CNN as she touted her climate change and clean-energy agenda.

“I’m the only candidate [who] has a policy about how to bring economic opportunity, using clean renewable energy as the key, into coal country. Because we’re going to put a lot of coal miners and coal companies out of business,” she said. “We’re going to make it clear that we don’t want to forget those people.”

She came under fire from the coal industry, which noted that coal keeps the lights on in Missouri, Ohio and Illinois, where Mrs. Clinton was locked in tight races with Mr. Sanders.

By Monday night Mrs. Clinton released a statement that reaffirmed her commitment to coal miners as she works to transform America into a “clean energy superpower.”

“I firmly believe that if you spent your life keeping the lights on for our country, we can’t leave you in the dark,” she said. “We need to use every tool we have to build a 21st century energy future that doesn’t leave anyone out or behind.”

• Seth McLaughlin and Kelly Riddell contributed to this report.

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