Write an inequality to represent this real-world situation. Andre wants to practice the piano 9 hours a week. Each time he practices he practices for 23

Question

2
3
hour. If he has already practiced 2 hours this week, how many sessions, x
𝑥
, does he still need to practice to reach or surpass his goal?(1 point).....

Answer 1

To find the inequality that represents Andre's situation, we start by defining the total time he wants to practice and how he practices.

Andre's goal is to practice a total of 9 hours in a week. He has already practiced for 2 hours and practices for \( \frac{23}{3} \) hours per session.

Let \( x \) be the number of practice sessions he still needs to complete.

The total time he will have practiced after \( x \) sessions is:

\[ \text{Total Practice Time} = \text{already practiced} + \text{time for } x \text{ sessions} \]

This can be expressed as:

\[ 2 + x \cdot \frac{23}{3} \]

Since he wants to practice at least 9 hours, we can set up the following inequality:

\[ 2 + x \cdot \frac{23}{3} \geq 9 \]

This inequality represents the requirement that Andre's total practice time needs to be at least 9 hours. To summarize, the inequality is:

\[ 2 + x \cdot \frac{23}{3} \geq 9 \]