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] 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]

Let's tackle the problem step by step!

We want to find the inequalities that represent the number of songs, [tex]$ m $[/tex], Miguel can purchase with his [tex]$25 gift card.

1. Understanding the Costs:
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.

2. Total Money Miguel Has:
Miguel has a total of $[/tex]25 on his gift card.

3. Setting Up the Inequality:
- The total cost of buying [tex]$ m $[/tex] songs is represented by the expression: [tex]$ 1.00 + 1.50 \times m $[/tex].
- Miguel can spend at most [tex]$25, so the expression $ 1.00 + 1.50 \times m $ should be less than or equal to 25. This gives us our first inequality:
\[
1 + 1.5m \leq 25
\]

4. Testing Total to be Strictly Less Than:
- Additionally, we consider the case where the total cost should be strictly less than $[/tex]25. This results in:
[tex]\[
1 + 1.5m < 25
\][/tex]

5. Form the Options as Inequalities:
- The two inequalities that accurately represent the situation are:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]

These inequalities define the maximum number of songs Miguel can purchase while considering the activation fee and the cost per song.