To determine the maximum number of meals the teacher can purchase with up to $180, let \( x \) represent the number of meals. Each meal costs $8.99. The inequality can be set up as follows:
\[ 8.99x \leq 180 \]
This inequality states that the total cost of the meals (which is $8.99 multiplied by the number of meals \( x \)) must not exceed $180.
Thus, the correct inequality that describes the situation is:
\[ 8.99x \leq 180 \]