Question

the arrowhead choir is practicing for a show. to feel prepared, they will practice for more than 22 hours. they also dont want to overuse their voices, so they will practice for less than 28 hours. so far, they have practiced a total of 10 hours. let x be the number of hours per week they will practice for the remaining 3 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.
(b) on the number line below, graph the solution that represents the possible numbers of hours per week they will practice.

Explanation:

Step1: Define total practice hours

Total practice hours = $10 + 3x$

Step2: Set up lower bound inequality

Total > 22, so $10+3x > 22$
Subtract 10: $3x > 12$
Divide by 3: $x > 4$

Step3: Set up upper bound inequality

Total < 28, so $10+3x < 28$
Subtract 10: $3x < 18$
Divide by 3: $x < 6$

Step4: Combine into compound inequality

Combine the two results: $4 < x < 6$

Step5: Explain number line graph

For $4 < x < 6$, plot open circles at 4 and 6, shade the region between them.

Answer:

(a) $\boldsymbol{4 < x < 6}$
(b) On the number line:

• Draw an open circle at 4 and an open circle at 6.
• Shade the segment of the number line that lies between these two open circles.