The operation $\odot$ is defined as $a \odot b = a + \frac{3a}{2b}$. What is the value of $8 \odot 6$?
We have $8\odot 6 = 8+\frac{3(8)}{2(6)}=8+2=\boxed{10}$.
10
Level 1
Algebra
Problem: The operation $\odot$ is defined as $a \odot b = a + \frac{3a}{2b}$. What is the value of $8 \odot 6$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of $8 \odot 6$, we need to apply the operation defined by the formula $a \odot b = a + \frac{3a}{2b}$. Here, we will substitute $a$ with $8$ and $b$ with $6$. 

First, we calculate the term $\frac{3a}{2b}$:

1. Substitute $a = 8$ and $b = 6$ into the expression:
   \[
   \frac{3 \cdot 8}{2 \cdot 6}
   \]

2. Calculate the numerator:
   \[
   3 \cdot 8 = 24
   \]

3. Calculate the denominator:
   \[
   2 \cdot 6 = 12
   \]

4. Now, divide the numerator by the denominator:
   \[
   \frac{24}{12} = 2
   \]

Next, we substitute this result back into the operation definition:

5. Now, we have:
   \[
   8 \odot 6 = 8 + 2
   \]

6. Finally, perform the addition:
   \[
   8 + 2 = 10
   \]

Thus, the final answer is $10$.<|END_OF_LATENT|> The final answer is $10$.