To solve this problem, we need to determine how many sets of glasses Violet needs to buy in order to have at least 800 glasses in total.
Let x be the number of sets of glasses Violet could buy.
Since each set on sale contains 6 glasses, the number of glasses Violet will have after buying x sets is 6x.
The total number of glasses needed is 800.
To form an inequality, we can say that the number of glasses Violet has after buying x sets must be greater than or equal to 800.
Therefore, the inequality becomes:
6x + 164 ≥ 800.
To solve this inequality for x, we can subtract 164 from both sides:
6x ≥ 800 - 164.
Simplifying, we have:
6x ≥ 636.
Finally, we divide both sides by 6 to solve for x:
x ≥ 636 / 6.
This simplifies to:
x ≥ 106.
Therefore, Violet needs to buy at least 106 sets of glasses to have enough for the restaurant.