Question

A student rode a bicycle fewer than 30 miles during a period of 5 days. The student rode 8 miles on Monday and m miles each day from Tuesday through Friday.
Which inequality represents all possible values of m?

Answer 1

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 \( m \):

1. Subtract 8 from both sides:

\[
4m < 30 - 8
\]

\[
4m < 22
\]

2. Divide both sides by 4:

\[
m < \frac{22}{4}
\]

\[
m < 5.5
\]

Thus, the inequality that represents all possible values of \( m \) is:

\[
m < 5.5
\]