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]$25 \geq 1 + 1.5m$[/tex]

B. [tex]$1 + 1.5m \leq 25$[/tex]

C. [tex]$1 + 1.5m < 25$[/tex]

D. [tex]$25 > 1 + 1.5m$[/tex]

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

To solve this problem, let's break down the situation step by step.

1. Understanding the Problem:
- Miguel has a [tex]$25 gift card.
- Each song costs $[/tex]1.50.
- There is a [tex]$1.00 activation fee for the account.

2. Define the Costs:
- If Miguel wants to buy `m` songs, the total cost will include the activation fee plus the cost of the songs.
- The total cost can be represented by the expression: $ 1 + 1.5m $.

3. Setting Up the Inequality:
- We need to ensure that this total cost does not exceed the gift card amount, which is $[/tex]25.
- This can be written as:
[tex]\[
1 + 1.5m \leq 25
\][/tex]

4. Analyzing the Inequality:
- This inequality ensures that the total spending (activation fee + the cost of the songs) stays within the limits of the gift card.

5. Alternative Representation:
- Another way to express this would be:
[tex]\[
1 + 1.5m < 25
\][/tex]
- This second inequality is slightly stricter, ensuring the total cost is less than $25, which still satisfies the condition.

In summary, two inequalities can represent this situation:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]

These inequalities account for both possibilities of spending all or slightly less than the total gift card value.