An exemplary web of preformed bags includes first and second layers, first and second side, first and second side seals proximate the first and second edges, a plurality of transverse seals extending between the first and second side edges, an opening in the first layer, and a line of separation in the second layer, and first and second cuts in the first and second side seals. The first and second cuts are configured to reduce or eliminate a breaking force necessary to break the first and second side seals when the web is torn along the line of separation.