What happens to the inequality when you multiply or divide by a negative number?

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Study for the Algebra 1 Honors End-of-Course Test. Study with flashcards and multiple-choice questions, each question has hints and explanations. Get ready for your exam!

Multiple Choice

What happens to the inequality when you multiply or divide by a negative number?

Explanation:
When you multiply or divide both sides of an inequality by a negative number, the inequality sign must flip. Negating values reverses their order on the number line, so the relationship between the two sides changes direction after the operation. For example, starting with 7 > 3, multiplying both sides by -2 yields -14 < -6, showing the sign must flip. In general, if a < b and you multiply by a negative number, ac > bc; if a > b and you divide by a negative number, ac < bc. The sign stays the same only when you multiply or divide by a positive number.

When you multiply or divide both sides of an inequality by a negative number, the inequality sign must flip. Negating values reverses their order on the number line, so the relationship between the two sides changes direction after the operation. For example, starting with 7 > 3, multiplying both sides by -2 yields -14 < -6, showing the sign must flip. In general, if a < b and you multiply by a negative number, ac > bc; if a > b and you divide by a negative number, ac < bc. The sign stays the same only when you multiply or divide by a positive number.

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