Fairfax County’s Board of Supervisors agreed Friday to the major components of a 2016 budget that would keep the property tax rate the same but leave school officials and county employees frustrated.

The nearly $4 billion spending plan includes about $2 billion for schools, $14 million less than educators sought, and trims a promised raise for county employees from the rate of inflation — 1.68 percent — to 1.1 percent.

The raise is more than the 0.84 percent proposed this year by County Executive Edward L. Long Jr. but less than what the county agreed to during labor negotiations this fall.

“We thought we had a deal in September,” said Randy Creller, the county’s chief labor representative. “They’ve broken that deal.”

Several board members offered some reason for optimism, however, saying they may be willing to compromise on the raise issue before the final vote on the budget on April 28.

Reneging on a labor deal, said Supervisor Michael R. Frey (R-Sully), sends the message that “we’re not willing to put our money where our mouth is.”

Although additional changes could come at a board meeting on Tuesday, overall the supervisors left the $3.81 billion spending plan Long proposed in February mostly intact.

The residential property tax rate would remain at $1.09 per $100 of assessed value, but because of increases in home assessments, homeowners would see an average property tax increase of $185.

Using an extra $2.7 million in state funds that officials learned about after Long proposed his budget, the board agreed to save some services that had been targeted for cuts, including $1.8 million in funding for a program aimed at preventing child abuse.

The board also found $120,000 to sustain a team of six part-time “engineering technicians” who investigate about 1,800 complaints of sloppy yards each year.

“This has been a tough budget season, but I think we’ve got a good package here,” said Sharon Bulova (D), the board’s chairman.

Budget negotiations were shaped by relatively weak revenue projections, a result of cuts in federal spending that have led to thousands of job losses in the region; a high office vacancy rate; and declining commercial tax revenue.

At the same time, Fairfax officials faced demands from a growing school system, more pressure from county unions for salary increases and an unwillingness among homeowners to pay higher property taxes.

The county board “has made our teachers and schools bear the burden of another shortfall in funding,” School Superintendent Karen Garza said in a statement. “The future of the excellence of Fairfax schools is significantly at-risk!”

Supervisors argued that there isn’t enough money to go around.

“We can all say we’re dissapointed, but nobody had an idea of how to find money that wasn’t there,” said Supervisor John C. Cook (R-Braddock).