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FLIP THE SIGN
Multiply or divide both sides by a negative number → flip < to > (or vice versa).
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DEFINE x FIRST
Always say "Let x = ___" before writing the inequality. Vague variables = wrong answers.
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COST vs REVENUE
For "cheaper at store A" problems: Cost_A < Cost_B. Include fixed travel/transport costs!
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INTEGER CHECK
If x must be a whole number, solve inequality then pick the smallest/largest integer that satisfies it.
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COMPOUND INEQ.
a < bx + c < d → solve both sides simultaneously. Keep the variable in the middle.
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SIGN OF COEFF.
If (a–b) < 0, dividing by (a–b) flips the inequality! Check whether a > b or a < b first.