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.

Question

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:

$$m<5.5$$