Republican front-runner Donald Trump spoke in Palm Beach, Fla., after primary voters took to the polls in five states: Florida, Illinois, Ohio, Missouri and North Carolina. (Reuters)

Republican front-runner Donald Trump spoke in Palm Beach, Fla., after primary voters took to the polls in five states: Florida, Illinois, Ohio, Missouri and North Carolina. (Reuters)

It was a good night for Donald Trump and an even better night for Hillary Clinton. On one of the most important days of the primary season, the two front-runners continued what has become an inexorable march to their party’s presidential nominations and a general election matchup that was unimagined when this campaign began.

For Clinton, it was a night to bounce back after her surprising defeat in Michigan at the hands of Sen. Bernie Sanders of Vermont last week. She did so in stunning fashion. With questions swirling about her candidacy, Clinton answered her critics with a series of victories that padded a lead in delegates that now has become almost insurmountable.

For Trump, it was a night in which he won at least three states and sent one rival, Sen. Marco Rubio of Florida, to the sidelines. But Trump was unable to put away a second, Ohio Gov. John Kasich. Like Clinton, the New York billionaire added to his delegate lead over Kasich and his nearest competitor, Sen. Ted Cruz of Texas. But the overall results still left open the prospect that the GOP nomination will not be decided until the party assembles in July in Cleveland for its national convention.

The night broke early in Clinton’s direction as she rolled to an overwhelming victory in Florida and followed that quickly with wins in North Carolina and Ohio. Early Wednesday, she added Illinois to her column. The first two were expected, given the makeup of the electorates in those states. Ohio’s demographics were close enough to those in Michigan to give Sanders hope of a repeat victory, but Clinton’s success dashed those hopes and blunted whatever momentum he had enjoyed.

The Ohio results represented a back-breaking blow to Sanders. His populist, anti-establishment insurgency has fired the energies of the party’s grass-roots progressives, and there is little doubt that he has both the determination and the resources to keep fighting. His campaign has accomplished far more than almost anyone anticipated and he has shaped the issue agenda and the dialogue in the Democratic nomination contest.

Democratic front-runner Hillary Clinton spoke to supporters in West Palm Beach, Fla., after primary voters took to the polls in five states: Florida, Illinois, Ohio, Missouri and North Carolina. (Reuters)

For all those assets, Sanders has fallen behind in the unforgiving arithmetic of the way Democrats choose their nominees. Clinton’s lead has been built by taking advantage of states where the demographics tilt heavily in her favor, particularly those with substantial populations of African Americans, while holding Sanders close in the states he has won.

Clinton holds a lead of nearly 300 pledged delegates, those determined by the results of the primaries and caucuses. That is a bigger lead in pledged delegates than then-Sen. Barack Obama had in his epic battle against Clinton eight years ago. Her lead among so-called super delegates — party leaders and elected officials — is even more overwhelming.

Because Democrats award pledged delegates proportionally, Sanders needs not only a string of victories but also popular vote margins large enough to pick up delegates in bushel baskets, contest by contest. For those who have questioned the quality of Clinton’s campaign, there’s no doubting the effectiveness of her delegate-focused strategy.

Clinton’s victory speech in Florida gave the clearest sense so far that she now feels confident about how the nomination will end. Her message was aimed at a general-election contest against Trump. She excoriated the Republican front-runner repeatedly, drawing attention to what she called his negative and divisive campaign.

Trump’s victories were another reminder of his ability to overcome adversity. For the past five days he has been on the defensive, criticized for encouraging violence against protesters at his rallies. He also was the target of millions of dollars in negative ads in Florida. In the face of that, he swamped Rubio in Rubio’s home state and won North Carolina and Illinois, as well.

Trump was very much on the mind of Kasich, when he appeared before supporters and promised he would not take a low road to the highest office in the land. Kasich was winless until Tuesday night, and Ohio was a make-or-break test. His ebullience was emblematic of his personality but also underscored Kasich’s relief — and perhaps surprise — that he is now one of three remaining candidates for the GOP nomination.

Kasich’s path ahead is still perilous. His belief is that the victory in Ohio will fundamentally change the dynamic of the GOP race and that the anti-Trump forces will begin to coalesce around him now that Rubio is out. But there are few states that offer obvious victories.

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There is no way he can win a majority before Cleveland, and it’s almost certain that he will not even be the delegate leader by the time the primaries and caucuses end. His real hope for winning the nomination is to seize the prize at the convention in Cleveland. He needs time, and enough victories, to prove his worth and then rely on a deadlocked convention to choose him to prevent Trump from becoming the nominee.

Kasich has yet to prove he is a long-distance runner. That is not the case with Cruz, who like Trump is emblematic of the strength of the outsiders in the Republican race. The Texas senator was at risk of ending the night without a victory, with his last hope coming in Missouri, where he and Trump were in a tight race. The results left him even further behind Trump in delegates.

Cruz could yet become the true challenger to Trump. His campaign has even sketched out a scenario under which he would end up with more delegates than Trump heading into the convention. But that depends on his ability to corner Trump in a one-on-one battle in the remaining states.

Some national polls have shown that when matched head-to-head against Trump, Cruz enjoys more support. That is the foundation on which the Cruz camp is building its strategy for winning the nomination. His advisers see plenty of opportunities ahead and anticipate a big day on June 7, the final day of the primaries, when the biggest prize is California and its 172 delegates.

But that strategy suffered a setback on Tuesday when Kasich won Ohio. Cruz’s advisers no doubt were privately pulling for Trump to do to Kasich what he did to Rubio. The Texas senator can ill afford a revived Kasich candidacy.

Cruz’s team also is confident that they can outperform Trump’s campaign in the combat that will take place at state party conventions over the coming weeks. It will be at those conventions that the delegates will be named. Cruz’s team will work every angle possible to fill slots with friendly delegates, even if many are pledged to Trump on the first ballot in Cleveland.

The establishment so far has failed to stop Trump and is now dependent on Kasich to do so. Cruz and his advisers are still trying to isolate Trump to give their strategy the ultimate test. They hope that even establishment Republicans rally behind the Texas senator now that the race is down to three.

Meanwhile, Trump is winning. He wins states, and he wins delegates. He has won in every region of the country, and his appeal to Republicans continues to be cross-cutting. It becomes ever harder to deny him the nomination.