Nicole needs to spend at least 4 hours each week practicing the guitar. She has already practiced two and one third hours this week. She wants to split the remaining practice time evenly between the last 2 days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of the 2 days.

a. two and one third + 2x ≥ 4
b. two and one third + 2x ≤ 4
c. two and one thirdx + 2 ≤ 4
d. two and one thirdx + 2 ≥ 4

1 answer

Nicole needs to spend at least 4 hours each week practicing the guitar, and she has already practiced \( \frac{7}{3} \) hours (which is two and one third hours). She will split the remaining practice time evenly between the last 2 days, meaning she will practice \( x \) hours each on those 2 days.

Let's write the inequality:

\[ \frac{7}{3} + 2x \geq 4 \]

This inequality states that the sum of the time she has already practiced (\( \frac{7}{3} \)) and the additional time she will practice over the last 2 days (2 times \( x \)) must be at least 4 hours.

In terms of the options provided:

a. two and one third + 2x ≥ 4

This is the correct inequality.

So, the correct answer is:
a. two and one third + 2x ≥ 4