A bracketing system is provided having two brackets joined by a flexible adhesive material that allows bridging or backing members of variable lengths and widths to be mounted between vertical studs to enhance stability of the wall construction. A wall construction assembly according to an embodiment of the invention comprises two vertical studs and a bridge backing member mounted there between by a bracketing system, which includes a left bracket and a right bracket connected by a flexible adhesive material. Because the bridge backing member can be adjustably sized to be secured on the brackets, it can be sized to fit between studs regardless of any variation in the spacing of the studs. This obviates the need to prefabricate bridge backing members to fit between variably spaced studs. The bridge backing member can be mounted flush with the stud to eliminate unevenness in the wall structure. Bridge or backing members of various widths and lengths can be mounted to the bracketing system.