Final answer:
The correct inequality to represent how much data your family can use without being charged more is d ≤ 5.
Step-by-step explanation:
The correct inequality to represent how much data your family can use without being charged more is D) d ≤ 5.
This inequality states that the amount of data used, represented by 'd', is less than or equal to 5. This means that as long as the data usage is 5 or less, your family will not be charged extra.
For example, if your family uses 3 gigabytes of data, which is less than 5, they will not be charged extra. However, if they use 6 gigabytes of data, which is greater than 5, they will be charged more.