Final answer:
The inequalities that can represent the situation are 1.50m + 1.00 ≤ 25 and 1.50m + 1.00 + x ≤ 25.
Step-by-step explanation:
To represent the situation where Miguel can use all or part of his $25 gift card to make a music purchase, we can use the following inequalities:
- Miguel can buy all songs and pay the activation fee: 1.50m + 1.00 ≤ 25
- Miguel can buy some songs and pay the activation fee: 1.50m + 1.00 + x ≤ 25, where x represents the remaining balance on the gift card
These inequalities account for the cost of each song, the activation fee, and the available budget of $25. Miguel can either buy all songs and pay the activation fee or buy some songs and have some balance remaining on the gift card.