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Inequality manipulationTechnique

Technique

Inequality manipulation

Solve like an equation; flip for negatives

3 min 3 steps

An inequality obeys equation rules right up until a negative shows up. Then it flips without warning, which I respect professionally.

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Calls on

Negative multipliers flip inequalitiesFactA negative multiplier reverses the inequality

Used by

Translate a situation into an equationTacticName each number's job, then write the equation
Solve linear equations for a targetTacticRead the target first, then stop when it stands alone
Model and optimize with inequalitiesTacticWrite the limit, solve at its edge, round to what fits
Solution-count and discriminant analysisTacticCollect everything on one side, then read one sign