The Fairfax County Board of Supervisors formally adopted a budget Tuesday for the next fiscal year that will add $357 to the average homeowner’s annual tax bill when higher property assessments are included.

The $3.7 billion budget raises the real estate tax rate by half a cent to $1.09 per $100 of assessed value and includes higher fees for sewer services and pet adoption, allowing for a 3.3 percent increase in spending over the current budget.

Nonetheless, it falls short in funding sought by the county school district, allocating an extra $51.5 million to the school system instead of the $98.1 million Superintendent Karen Garza said was needed to ward off drastic cuts and raise teacher pay.

The budget also reduces spending for some public services and environmental programs, cuts that supervisors agonized over as they sought to meet the demands of schools, county employees and others seeking more funding in what were often contentious budget talks.

“This was not an easy budget, and that’s an understatement,” board chairman Sharon Bulova (D) said, after a 7-3 vote to approve the new spending plan.

In what could lead to more revenue down the road, Bulova is convening a task force to consider placing before county voters a proposal to levy taxes on meals at restaurants and other eating establishments in the county.

Meanwhile, groups that had fought for more county money, in rallies and public hearings, were adjusting to the new spending plan.

Earlier this week, Garza proposed a revised schools budget that would reduce salary increases for district employees, among other adjustments, to account for the lower-than-requested amount of county funds. School and county officials anticipate that about $30 million in state funds for competitive teacher salaries would further close the gap.

County employees, who received a 2.29 percent pay increase under the new county budget, praised the board for that decision, though a spokeswoman with the local Service Employees International Union said they were pushing for even higher wages.

But in a statement, the union criticized the board for not increasing funding for some services.

“Demand for mental health and human services has risen dramatically recently, but the Board insists on asking us to do more with less,” Karen Conchar, the union’s secretary treasurer said in the statement.