To evaluate the expression [tex]\(2(x-4) + 3x - x^2\)[/tex] for [tex]\(x = 3\)[/tex], let's follow these steps:
1. Substitute [tex]\( x = 3 \)[/tex] into the expression:
[tex]\[
2(3-4) + 3 \cdot 3 - 3^2
\][/tex]
2. Simplify inside the parentheses first:
[tex]\[
3 - 4 = -1
\][/tex]
So the expression becomes:
[tex]\[
2(-1) + 3 \cdot 3 - 3^2
\][/tex]
3. Multiply constants next:
[tex]\[
2(-1) = -2
\][/tex]
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
3^2 = 9
\][/tex]
Now the expression is:
[tex]\[
-2 + 9 - 9
\][/tex]
4. Finally, perform the addition and subtraction:
[tex]\[
-2 + 9 = 7
\][/tex]
[tex]\[
7 - 9 = -2
\][/tex]
So, the value of the expression when [tex]\( x = 3 \)[/tex] is [tex]\(-2\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{-2} \][/tex]
