The number of points Aiden earns for each visit is 2.5, so the total number of points he earns after v visits is:
Total points = 75 + 2.5v
In order to get a free movie ticket, he needs at least 90 points. Therefore, we can write the inequality:
75 + 2.5v ≥ 90
Simplifying and solving for v:
2.5v ≥ 15
v ≥ 6
Therefore, Aiden needs to make at least 6 visits to the movie theater to earn enough points for a free movie ticket. The inequality representing this is:
v ≥ 6