Answer:
![\dfrac{30x}{24}>\dfrac{450}{24}](https://tex.z-dn.net/?f=%5Cdfrac%7B30x%7D%7B24%7D%3E%5Cdfrac%7B450%7D%7B24%7D)
Step-by-step explanation:
We are given the following in the question:
Let x be the total number of sparkling cans of water used in a day.
The family uses more than 15 cans each day so inequality becomes,
![x > 15](https://tex.z-dn.net/?f=x%20%3E%2015)
Number of cans in 30 days
![30x > 450](https://tex.z-dn.net/?f=30x%20%3E%20450)
The family buys case of water with 24 cans in each case.
Number of cans used in a day is more than 15, so approx number of cans used in 30 days will be =
![\dfrac{30x}{24}>\dfrac{450}{24}\\\\\Rightarrow \dfrac{30x}{24}>\dfrac{450}{24} = 18.75 \approx 19\\\\\text{Number of cases} > 19](https://tex.z-dn.net/?f=%5Cdfrac%7B30x%7D%7B24%7D%3E%5Cdfrac%7B450%7D%7B24%7D%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B30x%7D%7B24%7D%3E%5Cdfrac%7B450%7D%7B24%7D%20%3D%2018.75%20%5Capprox%2019%5C%5C%5C%5C%5Ctext%7BNumber%20of%20cases%7D%20%3E%2019)
Thus, the family buys around 19 cases or more of sparkling water in 30 days.