Final answer:
The absolute value equation to represent the minimum and maximum lengths of presentations, where x is the length, is |x - 29| <= 11. This equation signifies that the deviation of presentation length from the midpoint of 29 minutes must not exceed 11 minutes.
Step-by-step explanation:
To formulate an absolute value equation representing the range of presentation lengths between a minimum of 18 minutes and a maximum of 40 minutes, we define a variable x that represents the length of a presentation in minutes. To capture the idea that the length can deviate from a central point on both sides by a certain amount, we first need to identify that central point and the maximum deviation allowed from it.
The midpoint between 18 and 40 is calculated by averaging the two values:
Midpoint = (18 + 40) / 2 = 29 minutes.
The maximal deviation from this midpoint is the distance from the midpoint to either the minimum or the maximum length, which is:
Deviation = 40 - 29 = 11 minutes (or 29 - 18 = 11 minutes).
Consequently, our absolute value equation that represents the minimum and maximum lengths of the presentations is:
|x - 29| <= 11
This equation states that the absolute difference between the actual presentation length x and the midpoint of 29 minutes must be less than or equal to 11 minutes.