If $x@y=xy-2x$, what is the value of $(5@3)-(3@5)$?
$5@3=5\cdot3-2\cdot5=5$ and $3@5=3\cdot5-2\cdot3=9$, so $(5@3)-(3@5)=5-9=\boxed{-4}$. Another way to solve this problem is to realize that the expression $(5@3)-(3@5)$ is of the form $(x@y)-(y@x)=xy-2x-yx+2y=-2x+2y$, so the expression is just equal to $-2\cdot5+2\cdot3=\boxed{-4}$.
-4
Level 2
Algebra
Problem: If $x@y=xy-2x$, what is the value of $(5@3)-(3@5)$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of $(5@3)-(3@5)$, we first need to compute each operation defined by the expression $x@y=xy-2x$. 

Start with the first operation, $5@3$:
1. Substitute $x=5$ and $y=3$ into the operation: 
   $5@3 = 5 \cdot 3 - 2 \cdot 5$.
2. Calculate the multiplication: 
   $5 \cdot 3 = 15$.
3. Calculate the second term: 
   $2 \cdot 5 = 10$.
4. Now, subtract the second term from the first: 
   $15 - 10 = 5$.
Thus, $5@3 = 5$.

Next, compute the second operation, $3@5$:
1. Substitute $x=3$ and $y=5$ into the operation: 
   $3@5 = 3 \cdot 5 - 2 \cdot 3$.
2. Calculate the multiplication: 
   $3 \cdot 5 = 15$.
3. Calculate the second term: 
   $2 \cdot 3 = 6$.
4. Now, subtract the second term from the first: 
   $15 - 6 = 9$.
Thus, $3@5 = 9$.

Now, we can find the difference:
1. Substitute the results into the expression: 
   $(5@3) - (3@5) = 5 - 9$.
2. Perform the subtraction: 
   $5 - 9 = -4$.

The final answer is $-4$.<|END_OF_LATENT|> The final answer is $-4$.