Question

In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?

Answer 1

I’m pretty sure it’s 4 < r < 4.1
Please comment if you have any questions.

Answer 2

`4<r\leq 4.1`

Explanation:

We have been given that the radius of the gear, r, must be greater than 4 cm.

We can represent this information in an inequality as:

`r>4`

We are also told that the gear must not exceed 4.1 cm. We can represent this information in an inequality as:

`r\leq 4.1`

Upon combining both inequalities, we will get:

`4<r\leq 4.1`

Therefore, our required inequality is
`4<r\leq 4.1`.