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 + 15m \geq 25[/tex]

C. [tex]25 > 1 + 1.5m[/tex]

D. [tex]1 + 15m - 25[/tex]

E. [tex]25 \geq 1 + 1.5m[/tex]

To determine the number of songs Miguel can buy, considering the gift card and additional fee, we'll form inequalities based on the given conditions:

1. Understand the Costs:

- Activation fee: [tex]$ \$1.00 $[/tex]
- Cost per song: [tex]$ \$1.50 $[/tex]
- Gift card value: [tex]$ \$25 $[/tex]

2. Set Up the Inequality:

- The total cost for buying [tex]$ m $[/tex] songs includes the activation fee plus the cost for each song.
- Total cost: [tex]$ 1 + 1.5m $[/tex]
- This total cost must not exceed Miguel's gift card value, which is [tex]$ \$25 $[/tex].

3. Write the Inequalities:

- The inequality representing the maximum amount within the gift card is:
[tex]\[
1 + 1.5m \leq 25
\][/tex]

- We can also express this in another form by rewriting it as:
[tex]\[
25 \geq 1 + 1.5m
\][/tex]

4. Inequalities Validity Check:

- Both inequalities represent the same condition, just written differently.
- Based on these expressions, Miguel can purchase songs while ensuring the total cost doesn't exceed the gift card value.

Hence, the two inequalities that represent the situation correctly are:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 25 \geq 1 + 1.5m $[/tex]

These options ensure Miguel stays within the limit of his [tex]$ \$25 $[/tex] gift card after paying the activation fee and purchasing songs.