To determine which expression is NOT equivalent to \(9x + 4y + 13 - 3x - y - 10\), we first simplify the original expression.
Combine like terms:
\[ 9x - 3x + 4y - y + 13 - 10 \]
This simplifies to:
\[ (9 - 3)x + (4 - 1)y + (13 - 10) = 6x + 3y + 3 \]
Now we'll simplify each of the options to see which one is not equivalent to \(6x + 3y + 3\).
Option A: \(3(2x + y + 1)\)
Distributing the 3 gives:
\[ 3 \cdot 2x + 3 \cdot y + 3 \cdot 1 = 6x + 3y + 3 \]
Option B: \(6x + 3(1 + y)\)
Distributing the 3 gives:
\[ 6x + 3 \cdot 1 + 3 \cdot y = 6x + 3 + 3y \]
This is also \(6x + 3y + 3\).
Option C: \((9 - 3)x + (4 - 0)y + 3\)
Simplifying gives:
\[ 6x + 4y + 3 \]
This is NOT equivalent since we have \(6x + 4y + 3\) instead of \(6x + 3y + 3\).
Option D: \((13 - 10) + (9x - 3x) + (4y - y)\)
Calculating each term gives:
\[ 3 + 6x + 3y \]
This is equivalent to \(6x + 3y + 3\).
Thus, the expression that is NOT equivalent to \(9x + 4y + 13 - 3x - y - 10\) is:
C. \((9 - 3)x + (4 - 0)y + 3\)