To set up the inequality representing the total distance the student rode over the 5 days, we can organize the information as follows:
- Distance ridden on Monday: 8 miles
- Distance ridden from Tuesday to Friday: \(m\) miles each day for 4 days, which totals to \(4m\) miles.
The total distance ridden over the 5 days is then:
\[ 8 + 4m \]
Since the student rode fewer than 30 miles in total, we can express this as an inequality:
\[ 8 + 4m < 30 \]
To solve for \(m\), we can subtract 8 from both sides:
\[ 4m < 30 - 8 \]
\[ 4m < 22 \]
Now, we divide both sides by 4:
\[ m < \frac{22}{4} \]
\[ m < 5.5 \]
Thus, the inequality that represents all possible values of \(m\) is:
\[ m < 5.5 \]