To determine how many more sessions Bobby needs to practice, we start with the following information:
- Bobby wants to practice for at least 12 hours per week.
- He has already practiced for 3 hours.
- Each session lasts for three-fourths of an hour.
First, we need to find out how many hours Bobby still needs to practice to meet his goal.
The total hours he still needs is: \[ 12 \text{ hours} - 3 \text{ hours} = 9 \text{ hours} \]
Next, we need to convert the hours he still needs into sessions. Each session is \(\frac{3}{4}\) of an hour. To find out how many sessions \(s\) he needs, we set up the equation based on the relationship between sessions and hours practiced:
Since each session lasts \(\frac{3}{4}\) of an hour, the total number of hours practiced in \(s\) sessions will be: \[ \frac{3}{4}s \]
We want this to be at least 9 hours to meet or exceed the remaining practice goal. Therefore, we set up the inequality: \[ \frac{3}{4}s \geq 9 \]
To eliminate the fraction, we can multiply both sides of the inequality by 4: \[ 3s \geq 36 \]
Next, divide both sides by 3 to isolate \(s\): \[ s \geq 12 \]
Thus, the correct inequality that represents the situation is: \[ \frac{3}{4}s \geq 9 \] And from solving it, we conclude that Bobby needs at least 12 more sessions to meet or exceed his weekly practice goal.
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