Which rule must be applied when **dividing both sides of an inequality by a negative number**?
AThe inequality sign is preserved.
BThe inequality becomes an equation.
CBoth sides become zero.
DThe inequality sign is reversed (e.g. $<$ becomes $>$).
Answer & Solution
Correct answer: D. The inequality sign is reversed (e.g. $<$ becomes $>$).
Multiplying or dividing both sides by a **negative** number flips the inequality. Example: $-3 < -2$ but $(-3)(-1) = 3 > 2 = (-2)(-1)$.
Addition/subtraction by any number, and multiplication/division by a **positive** number, preserve the sign.
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