A student argues: *'For , . Multiplying both sides by gives . So .'* What is wrong with this argument?
Answer and explanation
Correct answer: A. Multiplying an inequality by reverses the inequality when is negative, and may be negative
- Step 1: The step is valid only if .
- Step 2: If then is automatically true, so negative values also satisfy the inequality. The solution is or .
Answer
Multiplying an inequality by reverses the inequality when is negative, and may be negative.
Why not the others: Multiplying by a positive number is fine, so the rule is not 'never allowed'. The inequality has solutions (for example and ). Dividing by would have the same sign problem, and was already excluded; the real flaw is the unknown sign of .
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