When you divide both sides of an inequality by a negative number, what happens to the inequality sign?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

When you divide both sides of an inequality by a negative number, what happens to the inequality sign?

Explanation:
Dividing by a negative number reverses the order of the inequality. If one side is larger than the other and you divide both sides by a negative value, the side that was larger becomes smaller after the division, so the inequality flips. For example, from 6 > 4, dividing both sides by -2 gives 6/(-2) = -3 and 4/(-2) = -2, which yields -3 < -2. The direction changed because of the negative divisor. This is why dividing by a negative number flips the inequality sign, while dividing by a positive number keeps the sign the same.

Dividing by a negative number reverses the order of the inequality. If one side is larger than the other and you divide both sides by a negative value, the side that was larger becomes smaller after the division, so the inequality flips.

For example, from 6 > 4, dividing both sides by -2 gives 6/(-2) = -3 and 4/(-2) = -2, which yields -3 < -2. The direction changed because of the negative divisor.

This is why dividing by a negative number flips the inequality sign, while dividing by a positive number keeps the sign the same.

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