When you multiply or divide both sides of an inequality by a negative number, you must change the direction of the inequality sign. This is because multiplying or dividing by a negative number reverses the order of the numbers involved. Here's a step-by-step explanation:
1. **Multiplying by a negative number:**
- For example, if you have the inequality 2 < -4 and you multiply both sides by -1, you get -2 > 4. The direction of the inequality sign changes from "<" to ">".
2. **Dividing by a negative number:**
- Similarly, if you start with the inequality -6 > 3 and divide both sides by -2, you end up with 3 < -1. Again, the direction of the inequality sign switches from ">" to "<".
Therefore, the statement "If I multiply or divide an inequality by a negative number, then I have to change the direction of the sign" is **True**. It is a crucial rule to remember when dealing with inequalities to ensure the correct representation of the relationship between the numbers involved.
