Question

Write and inequality for this real-world problem

Andre wants to practice piano 9 hours a week. Each time he practices he practices for 2/3 hour. If he has already practiced 2 hours this week how many sessions,x, does he still need to practice to reach or surpass his goal?

Answer 1

To write an inequality for Andre's practice sessions, let's first determine how many more hours he needs to practice after already practicing 2 hours this week.

1. **Total practice goal**: Andre wants to practice a total of 9 hours per week.
2. **Hours already practiced**: He has already practiced 2 hours.
3. **Remaining hours needed**: To find out how many hours he still needs to practice, we subtract the hours already practiced from the total goal:
\[
\text{Remaining hours} = 9 - 2 = 7 \text{ hours}
\]

4. **Practicing per session**: Each session of practice is \( \frac{2}{3} \) of an hour.
5. **Let \( x \)** be the number of additional sessions Andre needs to practice. The total hours he will practice in \( x \) sessions is:
\[
\text{Total practice hours in } x \text{ sessions} = \frac{2}{3}x
\]

6. **Setting up the inequality**: To find the number of sessions he needs to reach or surpass his goal of 9 hours, we set up the inequality:
\[
\frac{2}{3}x \geq 7
\]

This inequality \( \frac{2}{3}x \geq 7 \) represents the number of practice sessions, \( x \), that Andre still needs in order to reach or surpass his goal of practicing 9 hours this week.