To determine how many tickets Alex can buy without exceeding his budget, we start with the inequality given:
\[ 2t + 16 \leq 30 \]
Here, \( t \) represents the number of tickets Alex can buy. The $16 comes from his $8 admission and $8 spent on lunch.
Next, we solve the inequality step by step:
- Subtract 16 from both sides of the inequality:
\[ 2t \leq 30 - 16 \] \[ 2t \leq 14 \]
- Now, divide both sides by 2 to isolate \( t \):
\[ t \leq \frac{14}{2} \] \[ t \leq 7 \]
This means Alex can buy at most 7 tickets.
To summarize, the maximum number of ride tickets Alex can buy without spending more than $30 at the fair is 7 tickets.