Let's denote the number of basketballs Taylor can buy as \( b \).
Taylor's total budget is $125. She wants to buy one basketball jersey that costs $45. This means the amount of money she has left after buying the jersey is:
\[ 125 - 45 = 80 \]
The cost of each basketball is $12. Therefore, the total cost for \( b \) basketballs will be \( 12b \).
To find the maximum number of basketballs Taylor can buy without exceeding her budget of $80, we can set up the following inequality:
\[ 12b \leq 80 \]
This represents the condition that the total cost of the basketballs must be less than or equal to the remaining budget after buying the jersey.
To solve for \( b \), we divide both sides of the inequality by 12:
\[ b \leq \frac{80}{12} \]
This simplifies to:
\[ b \leq \frac{20}{3} \approx 6.67 \]
Since Taylor can only buy a whole number of basketballs, we take the largest whole number less than or equal to 6.67, which is 6.
Thus, the inequality that shows the maximum number of basketballs \( b \) that Taylor can buy is:
\[ 12b \leq 80 \]