LOS ANGELES - A key Boeing labor union narrowly approved late Friday an eight-year contract that keeps production of the new 777X jet airliner in Washington state in exchange for cuts in benefits. As a result, Boeing will stop seeking alternate sites for production of a more fuel-efficient version of its best-selling widebody jet.The Machinists Union District Lodge 751 said in a statement that members approved the controversial contract by 51 . “Our members have spoken and this is the course we’ll take,” said local union president Tom Wroblewski, who represents more than 30,000 hourly workers at Boeing. The contract was accepted even though Wroblewski and the local union leaders urged their members to reject Boeing’s offer, which they said included cuts in retirement and health care benefits, and set limits on future wage growth. “All along we knew that our members wanted to build the 777X,” Wroblewski said. “Now, it’s up to all of us now to pull together to make this airplane program successful.” When the union rejected a first offer from Boeing, the aerospace titan began to look elsewhere in the nation to move the program. Twenty-one other states, including California, Utah and Texas, quickly lined up with offers that included juicy tax breaks. The union vote means that Boeing will carry out final assembly and wing fabrication on the 777X at their sites in Puget Sound, in northwestern Washington state. “It was a tough vote, a hard situation, splitting the membership,” Mark Johnson, a national level official with the International Association of Machinists (IAM), told reporters. The 777X is a new version of Boeing’s successful 777 twin-engine widebody jet, which is built today in Everett. It is scheduled to come into service around 2020, and the company has already received billions of dollars in advanced orders. Boeing, founded in Seattle in 1916, has more than 82,000 employees in Washington state, making it the region’s largest private employer. A move elsewhere would likely have devastated the area economy.