To determine the minimum number of hours Maggie needs to practice on each of the 2 remaining days, we need to solve the problem step-by-step.
1. Identify Total Required Practice Time:
Maggie needs to spend at least 6 hours each week practicing the piano.
2. Determine Hours Already Practiced:
Maggie has already practiced [tex]\( 3 \frac{1}{4} \)[/tex] hours this week. Converting to decimal form:
[tex]\[
3 \frac{1}{4} = 3 + \frac{1}{4} = 3.25 \text{ hours}
\][/tex]
3. Set Up the Inequality:
Let [tex]\( x \)[/tex] represent the number of hours Maggie needs to practice on each of the remaining 2 days. The total practice time will be the sum of the hours already practiced and the additional hours she will practice over the 2 days. Since she needs to practice at least 6 hours in total:
[tex]\[
3.25 + 2x \geq 6
\][/tex]
4. Solve the Inequality:
[tex]\[
3.25 + 2x \geq 6
\][/tex]
Subtract 3.25 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x \geq 6 - 3.25
\][/tex]
Simplify the right side:
[tex]\[
2x \geq 2.75
\][/tex]
Divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x \geq \frac{2.75}{2}
\][/tex]
Simplify to get the minimum number of hours per day:
[tex]\[
x \geq 1.375
\][/tex]
Therefore, the correct inequality to determine the minimum number of hours Maggie needs to practice on each of the remaining 2 days is:
[tex]\[
3 \frac{1}{4} + 2x \geq 6
\][/tex]
So, Maggie needs to practice at least 1.375 hours each day for the remaining 2 days to meet her goal of practicing at least 6 hours in total for the week.
