Final answer:
Dividing each side of an inequality by the same positive number does indeed maintain the inequality's validity. The operation is similar to that used in equations and ensures the inequality remains balanced, provided the number used for division is positive.
Step-by-step explanation:
The question is asking whether dividing each side of an inequality by the same positive number maintains the inequality's validity, which is true. When performing operations on inequalities, you must do the same to both sides to maintain the inequality's balance. This rule is similar to handling equations; however, keep in mind that if you divide by a negative number, the inequality sign must be flipped. For instance, dividing both sides by a positive number maintains the direction of the inequality.
Let's consider an example to help clarify. If we have the inequality 10 > 5 and divide both sides by the positive number 2, we get 5 > 2.5, which is still true. The key is to ensure that the number you are dividing by is positive. If it were negative, you would change the direction of the inequality sign.