Solving xyz/(2(3+y)+4) = 8: Understanding the Field of Application

To find the domain of the given equation $\frac{xyz}{2(3+y)+4}=8$, we need to ensure the denominator is not zero. This means solving $2(3+y) + 4 = 0$.

Let's solve this step-by-step:

• Step 1: Simplify the expression $2(3+y) + 4 = 0$.
• Step 2: Expand to $6 + 2y + 4 = 0$.
• Step 3: Combine like terms to get $2y + 10 = 0$.
• Step 4: Isolate the variable $y$. Subtract 10 from both sides: $2y = -10$.
• Step 5: Divide by 2 to solve for $y$: $y = -5$.

If $y = -5$, the denominator becomes zero, which makes the original expression undefined.

Therefore, the value of $y$ must not be $-5$ for the expression to be valid. In conclusion, the restriction on $y$ is that $y \neq -5$.

The correct answer choice is: $y \neq -5$.