To evaluate the expression [tex]\( 2(x-4) + 3x - x^2 \)[/tex] for [tex]\( x = 2 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 2 \)[/tex] into the expression:
[tex]\[
2(2-4) + 3(2) - 2^2
\][/tex]
2. Simplify each part of the expression:
- Calculate inside the parentheses first:
[tex]\[
2 - 4 = -2
\][/tex]
- The expression now looks like:
[tex]\[
2(-2) + 3(2) - 2^2
\][/tex]
3. Perform the multiplications:
- Multiply [tex]\( 2 \)[/tex] by [tex]\( -2 \)[/tex]:
[tex]\[
2 \times (-2) = -4
\][/tex]
- Multiply [tex]\( 3 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[
3 \times 2 = 6
\][/tex]
- The expression now looks like:
[tex]\[
-4 + 6 - 4
\][/tex]
4. Perform the subtraction and addition:
- Combine [tex]\( -4 \)[/tex] and [tex]\( 6 \)[/tex] first:
[tex]\[
-4 + 6 = 2
\][/tex]
- Then subtract [tex]\( 4 \)[/tex]:
[tex]\[
2 - 4 = -2
\][/tex]
So, the value of the expression [tex]\( 2(x-4) + 3x - x^2 \)[/tex] for [tex]\( x = 2 \)[/tex] is [tex]\(-2\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-2}
\][/tex]
