The Fairfax County Board of Supervisors approved a 2016 budget on Tuesday that keeps the property tax rate for homeowners the same and falls $14 million short of what county school officials were seeking for next year.

The budget, which the board approved in a 7-to-3 vote, keeps intact what the supervisors informally agreed to last week in a budget committee meeting. The board will vote to formally adopt the budget next week.

“This is not a great news package, but I think that it is responsible and responsive to the needs of our community and to the uncertain fiscal climate we are operating in,” Sharon Bulova (D), the board chairman, said before the vote.

In the nearly $4 billion spending plan, funding for county schools remains at the roughly $2 billion proposed by County Executive Edward L. Long Jr. — a $66.7 million increase over this year’s school transfer by the county.

The county’s 12,000 employees will receive cost-of-living raises of 1.10 percent — which is short of the actual 1.68 percent increase in the cost of living from last year. Employees will also receive individual salary increases related to performance and longevity with the county.

The budget also keeps the county’s rate on residential taxes at $1.09 per $100 of assessed value. However, it raises the rate in a special tax district for Tysons Corner by a penny to $0.05 per $100 of assessed value.

None of the supervisors were happy with the final result of a budget process that began when Long proposed a budget in February that he said was filled with bad choices resulting mostly from the lasting economic effects of federal spending cuts.

Before voting against the budget Tuesday, Supervisor Linda Q. Smyth (D-Providence) cited the extra financial burden on homeowners in her district who have seen assessments on their homes increase during the past year.

On average, those new assessments amount to an extra $185 in property tax bills for Fairfax homeowners, though it is higher in portions of the county where the real estate market has rebounded more aggressively.

Smyth said that, although the overall property tax rate is not going up this year, it has increased by 20 cents since 2008, which has hurt homeowners.

“That’s a lot of difference, and they’re not seeing their salaries go up,” Smyth said.

Other supervisors argued that the overall budget has more positives than negatives.

“I think everybody agrees that it’s not a great budget, but it’s what we got,” Penelope A. Gross (D-Mason) said.

Using an extra $2.7 million in state funds that were not included in Long’s budget, the board agreed to restore several services that were slated for cuts by the county executive — including a $1.8 million program meant to prevent child abuse and the enforcement of a popular grass ordinance that costs the county $120,000.

Next year’s budget will also include salaries for the board, amounting to an extra $102,000 in spending.

Currently, all board members receive $75,000 per year. Starting in January, the salaries will change to $95,000 for board members and to $100,000 for the board chairman.