In approving a ballot measure sought by Gov. Jerry Brown to raise taxes for several years, Californians took a step toward improving the state’s fiscal situation and avoiding education cuts.

According to the California Secretary of State’s website, 53.9% of voters backed the measure, Proposition 30, while 46.1% voted against it, with all votes counted except for provisional and some mailed-in ballots.

The approval is a significant victory for Mr. Brown, a Democrat, who has staked his governorship on a campaign to raise taxes to ease the effects of the state’s budget crunch.

“Last night, Californians made the courageous decision to protect our schools and colleges and strengthen the California dream,” Mr. Brown said in prepared remarks. “The people of California have put their trust in a bold path forward and I intend to do everything in my power to honor that trust.”

The campaign opposing the measure said in a statement: “While we are disappointed in the outcome of the campaign, the voters have spoken.”

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