Final answer:
To express the condition where a student can have at most 3 absences for the year to receive an attendance award in inequality form, the correct representation is x ≤ 3.
Step-by-step explanation:
To represent the situation where a student, x, can have at most 3 absences for the year in order to get an attendance award, we would use an inequality. The inequality to describe this condition would be x ≤ 3. This inequality tells us that the number of days a student is absent (x) should be less than or equal to 3. If a student is absent more than 3 days, they would not meet the criteria for the attendance award.
In mathematics, we use inequalities to compare different quantities. An inequality symbol, like ≤ or <, shows the relationship between two values. In this example, we are saying that the number of absence days (x) is either less than or equal to 3.
To further understand how to use inequalities, let's look at an example drawn from a different context. Imagine a Lake Tahoe Community College instructor is assessing student absenteeism in math classes. They may expect students to miss a certain number of classes based on past patterns. If the expected number is 3.5 days absent on average, as evidenced in an instructor's sample, we could say that a specific student, with x absences, should have x ≤ 3.5 to be below or at this average. In reality, though, for our initial example of the attendance award, the threshold is strictly 3 absences, hence x ≤ 3.