To determine the inequality that represents all possible values of \( m \), we start by setting up the problem based on the information given.
The student rode 8 miles on Monday and \( m \) miles on each of the next 4 days (Tuesday through Friday). Therefore, the total distance the student rode over the 5 days can be expressed as:
\[ \text{Total distance} = 8 + 4m \]
According to the problem, this total distance is fewer than 30 miles. We can express that as an inequality:
\[ 8 + 4m < 30 \]
Next, we will solve this inequality for \( m \):
- Subtract 8 from both sides:
\[ 4m < 30 - 8 \]
\[ 4m < 22 \]
- Divide both sides by 4:
\[ m < \frac{22}{4} \]
\[ m < 5.5 \]
Thus, the inequality that represents all possible values of \( m \) is:
\[ m < 5.5 \]