Question

The tonal eclipse choir is practicing for a show. to feel prepared, they will practice for more than 46 hours. they also don't want to overuse their voices, so they will practice for less than 64 hours. so far, they have practiced a total of 16 hours. let x be the number of hours per week they will practice for the remaining 6 weeks. (suppose they will decide to practice the same amount of time each week.) (a) find the possible numbers of hours per week they will practice. write your answer as a compound inequality solved for x?

Answer 1

The possible numbers of hours per week the tonal eclipse choir will practice are 5 to 8.

Step-by-step explanation:

The tonal eclipse choir wants to practice for more than 46 hours and less than 64 hours in total. They have already practiced for 16 hours. Let x be the number of hours per week they will practice for the remaining 6 weeks. Since they want to practice the same amount of time each week, the total number of hours they will practice in the remaining weeks is 6x. So we can write the inequality as:

46 < 16 + 6x < 64

To solve the inequality, we first subtract 16 from all parts of the inequality:

46 - 16 < 16 + 6x - 16 < 64 - 16

30 < 6x < 48

Then, we divide all parts of the inequality by 6 to solve for x:

30/6 < x < 48/6

5 < x < 8

Therefore, the possible numbers of hours per week they will practice are between 5 and 8, written as the compound inequality 5 < x < 8.