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Let's break down the inequality:

**Given inequality:**  
\[
132 + x > 304
\]

### Solving for \( x \):
1. Subtract 132 from both sides:
   \[
   x > 304 - 132
   \]
2. Simplifying:
   \[
   x > 172
   \]

This means that Belvedere needs to sell more than 172 additional flower boxes to reach a total of over 304 flower boxes.

### Analyzing the options:

1. **"Belvedere must sell at most 304 flower boxes to get his bonus."**  
   This is incorrect. The inequality specifies that he needs to sell *more* than 304 boxes, not at most 304.

2. **"Belvedere sold 132 flower boxes already and needs to sell x more to reach his goal of more than 304."**  
   This is the correct interpretation of the inequality. He has already sold 132 boxes and needs to sell more than 172 additional boxes to exceed 304.

3. **"Belvedere sold 132 flower boxes already and needs to sell x more to reach his goal of at least 304."**  
   This is incorrect because "at least 304" would imply \( x \geq 172 \), but the original inequality requires \( x > 172 \), meaning the goal is to exceed 304 boxes.

4. **"Belvedere sold 304 flower boxes and is hoping to sell another 132."**  
   This is irrelevant to the given inequality.

### Correct option:
The second option is correct:  
**"Belvedere sold 132 flower boxes already and needs to sell x more to reach his goal of more than 304."**

Would you like more details or have any questions?

Here are five related questions for further practice:
1. What would the inequality look like if Belvedere needed to sell *at least* 304 flower boxes?
2. How would the solution change if Belvedere had already sold 150 boxes instead of 132?
3. What happens if we change the inequality to \( 132 + x \geq 304 \)?
4. How would you graph the solution \( x > 172 \) on a number line?
5. How many total boxes will Belvedere have sold if he sells exactly 173 more?

**Tip:** Always carefully check the wording of inequalities to distinguish between "greater than" and "greater than or equal to" when solving problems.

Understand how to solve the inequality 132 + x > 304. This problem covers key algebraic concepts involving inequalities and subtraction. Suitable for students in Grades 6-8.

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