To determine the money the league raises, we first need to find the profit made from each shirt without considering the advertising cost. We do this by subtracting the cost to make each shirt from its selling price.
The selling price per shirt is \[tex]$14, and the cost to make each shirt is \$[/tex]7. Therefore, the profit made per shirt is:
[tex]\[ 14 - 7 = 7 \, \text{dollars} \][/tex]
Next, if the league sells [tex]\( n \)[/tex] shirts, the total profit from selling [tex]\( n \)[/tex] shirts is:
[tex]\[ 7 \cdot n \][/tex]
However, we must also account for the upfront advertising cost of \$55. This cost will need to be subtracted from the total profit made from selling the shirts. Hence, the expression representing the money that the league raises, after subtracting the advertising cost is:
[tex]\[ 7n - 55 \][/tex]
Thus, the correct expression is:
[tex]\[ (14 - 7)n - 55 \][/tex]
Looking at the given options, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
