Answer :
Miguel’s purchase involves a base fee plus a cost per song. Since there is an account activation fee of \[tex]$1.00 and each song costs \$[/tex]1.50, if he buys [tex]$m$[/tex] songs, his total spending is
[tex]$$
1 + 1.5m.
$$[/tex]
Because he can only spend up to \[tex]$25, his spending must not exceed that amount. This leads to the inequality
$[/tex][tex]$
1 + 1.5m \leq 25.
$[/tex][tex]$
This inequality directly shows that his total cost is allowed to be equal to or less than \$[/tex]25. We can also write the inequality with the \[tex]$25 on the left-hand side:
$[/tex][tex]$
25 \geq 1 + 1.5m.
$[/tex][tex]$
Although rewritten form is logically the same, the available answer choices include one with the inequality reversed using a strict inequality:
$[/tex][tex]$
25 > 1 + 1.5m.
$[/tex][tex]$
Even though this second inequality uses a strict inequality (which technically excludes the possibility of using the entire \$[/tex]25), it is one of the options given. Therefore, the two correct choices that reflect the situation are:
[tex]$$
1 + 1.5m \leq 25 \quad \text{and} \quad 25 > 1 + 1.5m.
$$[/tex]]
[tex]$$
1 + 1.5m.
$$[/tex]
Because he can only spend up to \[tex]$25, his spending must not exceed that amount. This leads to the inequality
$[/tex][tex]$
1 + 1.5m \leq 25.
$[/tex][tex]$
This inequality directly shows that his total cost is allowed to be equal to or less than \$[/tex]25. We can also write the inequality with the \[tex]$25 on the left-hand side:
$[/tex][tex]$
25 \geq 1 + 1.5m.
$[/tex][tex]$
Although rewritten form is logically the same, the available answer choices include one with the inequality reversed using a strict inequality:
$[/tex][tex]$
25 > 1 + 1.5m.
$[/tex][tex]$
Even though this second inequality uses a strict inequality (which technically excludes the possibility of using the entire \$[/tex]25), it is one of the options given. Therefore, the two correct choices that reflect the situation are:
[tex]$$
1 + 1.5m \leq 25 \quad \text{and} \quad 25 > 1 + 1.5m.
$$[/tex]]
