Joshua has a points card for a movie theater.
- He receives 60 rewards points just for signing up.
- He earns 5.5 points for each visit to the movie theater.
- He needs at least 245 points for a free movie ticket.

Which inequality can be used to determine $v$, the minimum number of visits Joshua needs to earn his first free movie ticket?

Step 1 ：The problem is asking for an inequality that represents the minimum number of visits Joshua needs to make to the movie theater in order to earn his first free movie ticket.

Step 2 ：We know that Joshua starts with 60 points and earns 5.5 points for each visit. We also know that he needs at least 245 points for a free movie ticket.

Step 3 ：So, we can represent the total points Joshua has as \(60 + 5.5v\), where \(v\) is the number of visits.

Step 4 ：Since Joshua needs at least 245 points for a free movie ticket, we can set up the inequality as \(60 + 5.5v \geq 245\).

Step 5 ：This inequality represents the condition that Joshua needs to meet or exceed in order to earn his first free movie ticket.

Step 6 ：Now, let's solve this inequality to find the minimum number of visits Joshua needs to make.

Step 7 ：The inequality that can be used to determine \(v\), the minimum number of visits Joshua needs to earn his first free movie ticket is \(60 + 5.5v \geq 245\). When we solve this inequality, we find that \(v \geq 34\).

Step 8 ：Therefore, Joshua needs to visit the movie theater at least \(\boxed{34}\) times to earn his first free movie ticket.