Final answer:
The absolute value inequality describing the possible heights of all the students in a class with the shortest student being 60 inches and the tallest student being 72 inches is |x - 66| ≤ 6, where x represents a student's height in inches. This encompasses all students with heights between 60 and 72 inches.
Step-by-step explanation:
If the shortest student in a class is 60 inches tall and the tallest student is 72 inches tall, an absolute value inequality can be used to represent the range of possible student heights in the class. The inequality will have to account for all students whose height is at least 60 inches but no more than 72 inches. The variable x will be used to represent a student's height.
An absolute value inequality that describes this situation is |x - 66| ≤ 6. This inequality states that the distance between a student's height (x) and the midpoint height (66 inches) is less than or equal to 6 inches, which includes all students between 60 and 72 inches tall.
Breaking this down further, for a student's height x:
- If x is less than 66, then 66 - x ≤ 6, which simplifies to x ≥ 60.
- If x is more than 66, then x - 66 ≤ 6, which simplifies to x ≤ 72.
So all students in the class will have heights x such that 60 ≤ x ≤ 72, which is the range of possible heights for the class members.