Jose practices the violin at least 12 hours per week. He practices for 3 fourths of an hour each session. If Jose had already practiced 3 hours in one week, how many sessions remain to meet or exceed his weekly practice goal?

SHOW THE INEQUALITY AND THE SOLUTION

1 answer

To find out how many practice sessions Jose needs to complete his goal, we first need to set up the inequality.

  1. Total practice goal: Jose wants to practice at least 12 hours per week.
  2. Time already practiced: Jose has already practiced for 3 hours this week.
  3. 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 \( x \).

  1. Subtract 3 from both sides:

\[ x \left(\frac{3}{4}\right) \geq 12 - 3 \]

\[ x \left(\frac{3}{4}\right) \geq 9 \]

  1. 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.