When solving inequalities, multiplying or dividing both sides by a negative number requires you to flip the inequality sign. For example, if you have $-2x > 6$, dividing by $-2$ gives you $x < -3$. Remember this crucial step to get the correct solution! Inequalities show a range of possible values rather than a single answer, which makes them super useful in real-world problems.
Match each term with its definition:
| Term | Definition |
|---|---|
| 1. Inequality | A. A value that, when substituted for a variable, makes the inequality true. |
| 2. Solution Set | B. A mathematical sentence showing the relationship between quantities that are not strictly equal. |
| 3. Variable | C. The set of all values that satisfy a given inequality. |
| 4. Coefficient | D. A symbol (usually a letter) that represents a number. |
| 5. Solution | E. A number multiplied by a variable. |
When solving inequalities, if you multiply or divide by a ______ number, you must ______ the inequality ______. This is because multiplying or dividing by a negative number changes the ______ of the numbers, and flipping the sign ensures the inequality remains ______. For example, if you have $-3x > 9$, you divide both sides by $-3$, and the inequality becomes $x < -3$.
Explain in your own words why it's necessary to flip the inequality sign when multiplying or dividing by a negative number. Give a specific numerical example to illustrate your explanation.
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