Inequality problems. Case analysis
Overview
Important
Case analysis in inequality problems involves dividing the problem into several mutually exclusive cases, each corresponding to a different range or condition for the variables involved. We solve the inequality separately in each case and then combine the results.
Important properties
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Cases must cover all possible situations (exhaustive).
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Cases must not overlap (mutually exclusive).
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Case analysis is especially useful when the inequality involves absolute values, piecewise functions, or expressions that change behavior based on variable values.