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]

Let's break down the problem and solve it step by step.

We know that:
- Miguel has a gift card worth [tex]$25.
- Each song costs $[/tex]1.50.
- There is a one-time account activation fee of [tex]$1.00.

We need to find how many songs, represented by $ m $, Miguel can buy without exceeding his gift card value.

Let's create an inequality to reflect this situation:

1. Calculate Total Cost:
The total cost is the sum of the account activation fee and the cost of the songs.
\[
\text{Total Cost} = 1.00 + 1.50 \times m
\]

2. Set the Inequality:
This total cost should be less than or equal to the total value of the gift card, which is $[/tex]25.
[tex]\[
1 + 1.5m \leq 25
\][/tex]

This represents the first inequality option where the total cost does not exceed the gift card value.

3. Find Another Inequality Form:
We can also express it as the total cost being strictly less than the gift card value:
[tex]\[
1 + 1.5m < 25
\][/tex]

Thus, Miguel's spending should satisfy either of these two inequalities:

- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]

Based on the options given, the correct choices are:
- [tex]$ 1 + 1.5m \leq 25 $[/tex]
- [tex]$ 1 + 1.5m < 25 $[/tex]

These two inequalities ensure that Miguel's total expenditure will stay within the limit of the gift card.