Problem

A value \(x\) stays within \(3~\text{units}\) of \(20\). Model A is \(|x-20|\le~3\), and Model B is \(x-20\le~3\). Evaluate \(\text{both}~\text{models}\) against the context. Report the valid model, the governing relationship, the feature that matches, and the mismatch in the rejected model.

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selected model=A; governing relationship=distance from20 is at least3; feature match=absolute value represents two-sided distance; rejected-model mismatch=B cannot represent values at least3 units from20

selected model=A; governing relationship=distance from20 is at most3; feature match=absolute value represents two-sided distance; rejected-model mismatch=B permits values arbitrarily far below20

selected model=B; governing relationship=distance from20 is at most3; feature match=x−20 measures that distance without absolute value; rejected-model mismatch=A adds an unnecessary absolute-value operation

selected model=B; governing relationship=x is no more than3 above20; feature match=x−20≤3 gives the upper limit; rejected-model mismatch=A unnecessarily includes values below20

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A value \(x\) stays within \(3~\text{units}\) of \(20\). Model A is \(|x-20|\le~3\), and Model B is \(x-20\le~3\). Evaluate \(\text{both}~\text{models}\) against the context. Report the valid model, the governing relationship, the feature that matches, and the mismatch in the rejected model.

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