To solve this problem, we need to follow several steps to determine how many hours Maggie must practice on each of the last two days to reach a total of at least 6 hours for the week.
1. Identify the minimum hours required:
Maggie needs to practice at least 6 hours in a week.
2. Determine how many hours she has already practiced:
Maggie has already practiced [tex]\( 3 \frac{1}{4} \)[/tex] hours. Converting this mixed fraction to a decimal, we get:
[tex]\[ 3 \frac{1}{4} = 3 + 0.25 = 3.25 \text{ hours} \][/tex]
3. Calculate the remaining hours needed:
To find out how many more hours she needs to practice, subtract the hours she has already practiced from the total required:
[tex]\[ 6 - 3.25 = 2.75 \text{ hours} \][/tex]
4. Distribute the remaining hours evenly over the last 2 days:
Maggie wants to split the remaining practice time equally over the last two days. Therefore, we need to find out how many hours per day she should practice:
[tex]\[ \frac{2.75}{2} = 1.375 \text{ hours per day} \][/tex]
5. Formulate the inequality:
To ensure that Maggie's total practice time meets or exceeds the required 6 hours, we can set up the following inequality:
[tex]\[ 3 \frac{1}{4} + 2x \geq 6 \][/tex]
So, the correct inequality that determines the minimum number of hours Maggie needs to practice on each of the last 2 days is:
[tex]\[ 3 \frac{1}{4} + 2x \geq 6 \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{3 \frac{1}{4} + 2x \geq 6} \][/tex]
