The Fairfax County Board of Supervisors, apparently calculating that it is wiser to appease taxpayers than public school teachers, is likely to cut taxes but shun teacher demands for higher salaries, according to county officials.

As the county board started three consecutive nights of public hearings on its $1.4 billion budget yesterday, supervisors were predicting that Fairfax homeowners will see their seventh reduction in the real estate tax rate in a decade, as well as a reduction of the personal property tax that county residents are required to pay on their motor vehicles and other items.

The real estate tax rate decrease, which is expected to amount to 3 to 5 cents per $100 of assessed value, would not fully offset higher property assessments for most county homeowners. It would, however, soften the blow to residents who have complained about sharply higher assessments.

If the county's real estate taxes remain at the current rate of $1.39 per $100 of assessed value, the taxes on a typical Fairfax home valued at $109,000 would rise by $54 to $1,516 because of increased assessments. A cut of 3 cents in the tax rate would still leave the same homeowner with a tax bill of $1,483, a $21 increase over his current bill; a 5-cent cut would roughly offset the average increase of 3.5 percent in residential assessments.

"I'm getting letters and phone calls urging the board to adjust the tax rate downward as a result of the rise in assessments," said Supervisor Nancy K. Falck (R-Dranesville).

On the personal property tax, the supervisors are predicting a cut of 15 to 20 cents from the current rate of $4.80 per $100 of assessed value. It would be the first decrease in recent years in the personal property tax, which covers airplanes and boats as well as motor vehicles.

Given the supervisors' determination to cut taxes and the shape of the county's budget, county officials agree it is unlikely that the county's 7,000 public school teachers will get the 8.8 percent across-the-board salary raise they are seeking.

Fairfax County Executive J. Hamilton Lambert's proposed fiscal 1987 budget, which takes effect July 1 this year, includes a 4 percent cost-of-living raise for all county and school employes. In addition, the school board has proposed raising the starting salary for a teacher with a bachelor's degree by 8.8 percent, to $20,000 a year.

The Fairfax County Education Association, a teachers' association, says that all teachers in the county should receive an 8.8 percent raise. Teachers in the Fairfax schools, the 10th largest school system in the nation, make an average annual salary of $29,000.

In support of their demands, the teachers have mounted a letter-writing campaign and are planning to picket the board's budget hearings. Several dozen speakers representing teachers, students and parents are expected to appear before the board to advocate higher teacher salaries.

Amid indications that the county board is unsympathetic to the teachers' demands, the FEA is threatening to take unspecified job actions.

Although strikes by public employes are illegal in Virginia, one association official refused to rule out that option in an interview. "Strikes are held in many states where strikes are illegal," said Mimi Dash, the president-elect of the FEA. "We are considering all possible options. We're not ruling out [striking]."