To determine the inequality that represents the total distance the student rode over the 5 days, we can start by adding the distance ridden on Monday to the distance ridden from Tuesday through Friday.
The distance ridden on Monday is 8 miles. The distance ridden from Tuesday to Friday (4 days) is represented as \( m \) miles per day. Therefore, the total distance ridden from Tuesday to Friday is:
\[ 4m \]
Now, we can express the total distance ridden over the 5 days as:
\[ 8 + 4m \]
According to the problem, the total distance is fewer than 30 miles. This gives us the inequality:
\[ 8 + 4m < 30 \]
To solve the inequality for \( m \), we can first subtract 8 from both sides:
\[ 4m < 30 - 8 \] \[ 4m < 22 \]
Next, we divide both sides by 4:
\[ m < \frac{22}{4} \] \[ m < 5.5 \]
Thus, the inequality that represents all possible values of \( m \) is:
\[ m < 5.5 \]
This indicates that the student can ride up to 5.5 miles each day from Tuesday to Friday.