Final answer:
The inequality to find all possible widths of a room when the perimeter must be greater than 72 feet is w > (72 - 2l) / 2, where l is the length of the room.
Step-by-step explanation:
To find the inequality that determines all possible widths (w) of a rectangular room given that the perimeter must be greater than 72 feet, we need to recall that the perimeter (P) of a rectangle is twice the sum of its length (l) and width (w), or P = 2l + 2w. If the perimeter must be greater than 72 feet, the inequality is 2l + 2w > 72.
We can simplify this inequality to solve for the width if the length is known. Assuming the length (l) is a constant value, the inequality can be rearranged to show the relationship between the width (w) and the required perimeter: w > (72 - 2l) / 2.
This inequality can then be used to find all possible values of width (w) that satisfy the condition of having the room's perimeter greater than 72 feet.