To find out how many practice sessions Jose needs to complete his goal, we first need to set up the inequality.
- Total practice goal: Jose wants to practice at least 12 hours per week.
- Time already practiced: Jose has already practiced for 3 hours this week.
- Time he practices per session: Each practice session lasts for \(\frac{3}{4}\) of an hour.
Let \( x \) be the number of additional sessions Jose needs to complete.
The total practice time Jose will have after \( x \) sessions can be expressed as follows:
\[ \text{Total practice time} = 3 \text{ hours} + x \left(\frac{3}{4} \text{ hours/session}\right) \]
To meet or exceed the practice goal of 12 hours, we set up the following inequality:
\[ 3 + x \left(\frac{3}{4}\right) \geq 12 \]
Next, we need to solve this inequality for \( x \).
- Subtract 3 from both sides:
\[ x \left(\frac{3}{4}\right) \geq 12 - 3 \]
\[ x \left(\frac{3}{4}\right) \geq 9 \]
- Next, multiply both sides by \(\frac{4}{3}\) to solve for \( x \):
\[ x \geq 9 \left(\frac{4}{3}\right) \]
\[ x \geq 12 \]
Thus, Jose needs at least 12 additional sessions to meet or exceed his weekly practice goal.
Final answer: Jose has 12 sessions remaining to meet or exceed his weekly practice goal.