When multiplying or dividing by a negative number, the inequality sign must be ___.
1. removed
2. flipped
Whenever you multiply or divide the inequality by a negative number, you have to flip the inequality sign.
2. flipped.
When multiplying or dividing by a negative number, the inequality sign must be flipped.
To understand why this is the case, we need to consider the effect of multiplying or dividing by a negative number on an inequality.
Multiplying or dividing by a negative number essentially reverses the direction of the inequality. Let's say we have the inequality x > 3. If we multiply both sides of the inequality by -2, we get -2x < -6. Notice that the inequality sign flipped from "greater than" to "less than." This is because multiplying by a negative number changes the direction of the inequality.
Similarly, dividing both sides of an inequality by a negative number leads to a flipped inequality sign. For example, if we have the inequality -5x < 10, and we divide both sides by -5, we obtain x > -2. Again, the inequality sign flipped from "less than" to "greater than."
So, when multiplying or dividing an inequality by a negative number, we must flip the inequality sign to maintain the correct direction of the inequality. Therefore, the correct answer is option 2: flipped.