A thin uniform rectangular plate of mass M and width w is mounted so it can rotate about an axis parallel to its height and lying in the plane of the plate at a distance x from its center of mass. The design requires that the rotational inertia about this axis not exceed 1.5 times the rotational inertia Icm=121Mw2 about the central axis parallel to the height. Derive the inequality that limits x and determine the maximum allowable value of x in terms of w.