If objects of weights x and w₁ 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 w₁ such that the cross-beam is horizontal. If a and b are not known precisely, we might proceed as follows. First balance x by w₁ on the left, as in (A). Then switch places and balance x by w₂ on the right, as in (B). The average x̅ = 12 (w₁ + w₂) gives an estimate for x. Show that ¯x is greater than or equal to the true weight x.

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WI O (A) (B) b W2