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The problem states that the parking meter charges $2 initially for the space and then $0.75 per hour after that. Nath has a maximum of $5 to spend. The question is asking which inequality represents the situation where Nath can park for a certain number of hours, denoted by $ x $.

### Breakdown of the charges:
- Fixed cost: $2 for the parking space.
- Variable cost: $0.75 per hour for each additional hour of parking.

The total amount Nath can spend is at most $5. Thus, the inequality should represent that the total parking cost (the $2 initial fee plus $0.75 times the number of hours) must be **less than or equal to** $5, since Nath cannot exceed this amount.

### Correct inequality:
\[
2 + 0.75x \leq 5
\]

This inequality correctly describes the situation where the total cost is at most $5. Therefore, the correct option is:

**Option 3: $ 2 + 0.75x \leq 5 $**

Would you like further details or clarifications?

### Related Questions:
1. How would the inequality change if Nath had $10 instead of $5?
2. What would be the maximum number of hours Nath can park with $5?
3. How would the inequality change if the hourly rate increased to $1?
4. Can Nath park for 4 hours with $5?
5. How would you solve this inequality for $ x $ to find the maximum number of hours?

### Tip:
When solving word problems, always identify fixed and variable costs, then write an equation or inequality that describes the total cost.

The parking meter charges $2 for the parking space, then $0.75 each hour. Nath only has $5. Which inequality can be used to determine the number of hours he can park?

Learn how to solve a real-world linear inequality problem. Given the parking meter charges of $2 for the initial fee and $0.75 per hour, Nath needs to determine how many hours he can park with a maximum budget of $5. This problem introduces key algebraic concepts, including formulating and solving inequalities.

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