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?

1 answer

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:

\[ 4m < 30 - 8 \]

\[ 4m < 22 \]

  1. Divide both sides by 4:

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

\[ m < 5.5 \]

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

\[ m < 5.5 \]