Industry mini-project: double booking of GPU slots

Students book 2-hour slots on the EdgeCampus GPU server through a web app running on three application servers behind a load balancer, sharing one MySQL database. The booking code is:

// 1. check
int n = jdbc.queryForObject("SELECT COUNT(*) FROM bookings WHERE gpu = ? AND slot = ?", Integer.class, gpu, slot);
if (n == 0) {
    // 2. act
    jdbc.update("INSERT INTO bookings(gpu, slot, student) VALUES (?, ?, ?)", gpu, slot, student);
}

At 8:00 on Monday, when bookings open, some slots end up booked twice.

1. Explain the race with a timeline involving two servers.
2. Explain why adding synchronized to the Java method does not fix it.
3. Propose three correct solutions at different levels (database constraint, transaction/locking, distributed lock or queue) and compare them (correctness, performance at 8:00, complexity, failure behaviour).
4. How would you test that the fix works?