Miguel can use all or part of his [tex]\$25[/tex] gift card to make a music purchase. Each song costs [tex]\$1.50[/tex], and there is a [tex]\$1.00[/tex] per account activation fee.

Which inequalities can represent this situation if [tex]m[/tex] is the number of songs he can buy? Select two options.

A. [tex]1 + 1.5m \leq 25[/tex]
B. [tex]1 + 1.5m \geq 25[/tex]
C. [tex]25 > 1 + 1.5m[/tex]
D. [tex]1 + 1.5m < 25[/tex]
E. [tex]25 \geq 1 + 1.5m[/tex]

To solve this problem, we need to understand the costs involved in Miguel's music purchase and represent these using inequalities.

1. Identify the components:
- Miguel has a gift card worth [tex]$25.
- Each song costs $[/tex]1.50.
- There is a fixed account activation fee of [tex]$1.00.

2. Write an inequality:
- The total cost for buying `m` songs is the sum of the account activation fee plus the cost of the songs.
- Therefore, the total cost is: $ \text{Total Cost} = 1 + 1.5m $.
- This total cost has to be less than or equal to the $[/tex]25 gift card, which can be written as:
[tex]\[
1 + 1.5m \leq 25
\][/tex]

3. Rearrange the inequality if needed:
- You may also write this inequality in another form:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]

Both these inequalities represent the same situation and show the maximum number of songs Miguel can purchase, considering he cannot exceed the $25 balance on his gift card after paying an account activation fee.

4. Selecting the options that match our inequalities:
- From the choices given, the correct expressions are:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 25 \geq 1 + 1.5m $[/tex]

These two options correctly represent the constraints on the number of songs Miguel can buy.