The ornamental design for an adjustablewall-mounted appliance support, as shown and described.
FIG. 1 is a top, front, and right side perspective view of an adjustable
wall-mounted appliance support showing our new design, the broken-line
depiction of a television set being for illustrative purposes only and
forming no part of the claimed design;
FIG. 2 is a left side elevational view thereof, the right side being a
mirror image of that shown;