DETROIT — A judge has given Detroit the green light to cut pensions as a way out of the largest municipal bankruptcy in U.S. history, a decision that puts the case in the laps of thousands of retirees who had hoped the Michigan Constitution would protect them from getting smaller checks in their golden years.

Judge Steven Rhodes said the city is eligible to stay in bankruptcy court and scrub $18 billion in debt, about half of that amount linked to underfunded pensions and health care obligations. But he also warned officials that they’ll need to justify any deep reductions.

The case now turns to crunching numbers and trying to strike deals, although unions are pursuing an appeal.

Some retirees said they felt socked by the outcome.

“We’ll be thrown out of our homes and starving if they seriously slash our pensions. Then they’ll tell us to go to the soup lines,” said David Sole, 65, who retired from the public works department in January after 22 years and whose wife also is a city retiree.

“We don’t know what they are going to take,” Sole said. “The judge said he would not tolerate steep cuts. What’s steep?”

The judge, who wondered aloud why the bankruptcy had not happened years ago, said pensions can be altered just like any contract because the state constitution does not offer bulletproof protection for public employee benefits. But he signaled a desire for a measured approach and warned city officials that he would not “lightly or casually” sign off on just any cuts.

“This once proud and prosperous city can’t pay its debts. It’s insolvent,” Rhodes said in formally granting Detroit the largest public bankruptcy in U.S. history. “At the same time, it also has an opportunity for a fresh start.”

The ruling came more than four months after Detroit filed for Chapter 9 protection.