To solve this problem, we need to determine the minimum number of hours Nicole needs to practice on each of the remaining 2 days of the week to reach her goal of 4 hours of practice in total for the week. Let's break down the problem step-by-step.
1. Identify the total required practice time:
- Nicole needs to practice at least 4 hours each week.
2. Determine the amount of time already practiced:
- Nicole has already practiced [tex]\(2 \frac{1}{3}\)[/tex] hours.
3. Represent the already practiced time in decimal form:
- [tex]\(2 \frac{1}{3} = 2 + \frac{1}{3} \approx 2.3333333333333335\)[/tex] hours.
4. Define the variables:
- Let [tex]\(x\)[/tex] be the number of hours Nicole needs to practice on each of the remaining 2 days.
5. Set up the inequality to represent the total practice time:
- Nicole's total practice time is the sum of the time she has already practiced and the additional time she will practice over the next 2 days.
- Therefore, the inequality is: [tex]\(2.3333333333333335 + 2x \geq 4\)[/tex].
Given the answer choices:
- [tex]\(2 \frac{1}{3} + 2x \geq 4\)[/tex] translates to [tex]\(2.3333333333333335 + 2x \geq 4\)[/tex], which matches our derived inequality. This indicates that this inequality accurately captures the situation described.
Thus, the correct inequality to determine the minimum number of hours Nicole needs to practice on each of the remaining 2 days is:
[tex]\[2 \frac{1}{3} + 2x \geq 4\][/tex]
