Solving for the force: mass 275kg and acceleration of -4.50m\s what happens to the negative sign?

Force = (mass) x (acceleration)

           = (275kg) x (-4.5 m/s²)  =  -1,237.5 newtons.

In order for this mass to experience acceleration of -4.5 m/s²,
it must be pushed by  -1,237.5 newtons of force, otherwise
it will not have that acceleration.

The plus and minus signs are completely your choice.  The
positive direction is the direction you decided to call positive
when you started working with the problem.  Chances are,
you probably called the positive direction the one in which
the object is already moving.  That makes the acceleration
positive if the object is speeding up, negative if it's slowing
down. 

If the acceleration is positive (speeding up), that means the
object is being pushed by a force in the same direction it's
already moving.  If the acceleration is negative (slowing down),
that means the object is being pushed by a force opposite to
the direction it's already moving ... the negative direction.