51. If objects of weights x and wi are suspended from the balance in Figure 14(A), the cross-beam is horizontal if bx = aw1. If the lengths a and b are known, we may use this equation to determine an unknown weight x by selecting wi such that the cross-beam is horizontal. If a and b are not known precisely, we might proceed as follows. First balance x by wi on the left as in (A). Then switch places and balance x by uwz on the right as in (B). The average = (w1 + w2) gives an estimate for x. Show that i is greater than or equal to the true weight x. (A) (B) FIGURE 14

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