Final answer:
Bella should use the inequality 6x + 342 ≥ 759 to determine the minimum number of knife sets to purchase, which ensures the restaurant has at least 759 knives. The correct option among the provided choices is c) 6x + 342 ≥ 759.
Step-by-step explanation:
The question requires solving for the minimum number of sets of knives Bella must buy to ensure the restaurant has at least 759 knives. We can set up an inequality to represent this scenario. The restaurant already has 342 knives, and each set Bella can buy contains 6 knives. The variable x represents the number of sets she needs to buy. We want the total number of knives after the purchase to be at least 759. Therefore, the inequality that correctly represents this situation is:
6x + 342 ≥ 759
To find the minimum number of sets needed, Bella would solve the inequality. Considering the possible choices:
a) 6(342+x) > 759 - This is incorrect because the inequality symbol is greater than, not greater than or equal to, and the variable x is incorrectly added inside the parentheses with 342.
- b) 6x + 342 < 759 - This is incorrect because the inequality symbol is less than, not greater than or equal to.
- c) 6x + 342 ≥ 759 - This is the correct inequality because it adds the current number of knives to 6 times the sets needed and requires it to be at least equal to 759.
- d) 6(342+x) < 759 - This is incorrect for the same reasons as option a, and also because the inequality symbol is less than.
So, the correct answer is c) 6x + 342 ≥ 759.