To determine the minimum number of hours Nicole needs to practice on each of the last 2 days to meet her weekly goal, we need an inequality that represents the total practice time for the week.
Let's break down the problem:
1. Nicole needs to practice at least 4 hours in total for the week.
2. She has already practiced 2 and one third hours, which can be written as \( \frac{7}{3} \) hours.
3. Let \( x \) be the number of hours she practices each of the last 2 days.
4. The total remaining practice time is therefore represented as \( 2x \).
The inequality would equate the total practice time she will have (the time she has already practiced plus the time she still needs to practice) to at least 4 hours. This can be represented as:
\[ \frac{7}{3} + 2x \geq 4 \]
So, the correct inequality is:
\[ \frac{7}{3} + 2x \geq 4 \]
Thus, the minimum number of hours she needs to practice on each of the 2 days is given by:
\[ \frac{7}{3} + 2x \geq 4 \]
Simplifying this inequality to find \( x \):
1. Subtract \( \frac{7}{3} \) from both sides to isolate \( 2x \):
\[ 2x \geq 4 - \frac{7}{3} \]
2. Convert 4 to a fraction with a common denominator:
\[ 4 = \frac{12}{3} \]
3. Perform the subtraction:
\[ 2x \geq \frac{12}{3} - \frac{7}{3} \]
\[ 2x \geq \frac{5}{3} \]
4. Divide both sides by 2:
\[ x \geq \frac{5}{6} \]
So, Nicole needs to practice at least \( \frac{5}{6} \) hours each of the last 2 days to meet her weekly practice goal.
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.
two and one third + 2x ≥ 4
two and one third + 2x ≤ 4
two and one thirdx + 2 ≤ 4
two and one thirdx + 2 ≥ 4
1 answer