Most speakers at a public hearing Wednesday night favored moving the Fairfax County government headquarters out of Fairfax City to a 266-acre tract two miles west of the city, but the County Board of Supervisors postponed until Monday its decision on whether to move.

On supervisor, Joseph Alexander (D-Lee), who said he favors the move, suggested cutting property taxes by redirecting $11 million tha he said is available in the county's operating budget forbuying a new govenment site. Alexander proposed selling bonds to raise the money for the new site and using the $11 million for other purposes. The result, he said, would be an average reduction of $55 in a homeowner's property tax bill.

The other supervisors took no action on Alexander's suggestion.

The site two miles west of Fairfax City known as the Smith-Carney tract, was recommended by a special citizen committed that studied relocation for a year. The committee said the county could sve $50 million over the next 40 years by moving out of Fairfax City, where it now spends $1 million a year renting space at 15 different locations.

Although most speakers favored the move to the Smith-Carney tract, several residents of adjacent communities said they would prefer no development at all there and expressed doubts that a county office complex would benefit their area.