To evaluate the expression [tex]\(4(x-3) + 5x - x^2\)[/tex] for [tex]\(x = 5\)[/tex], follow these detailed steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the expression:
[tex]\[
4(5-3) + 5(5) - 5^2
\][/tex]
2. Simplify the expression inside the parentheses first:
[tex]\[
4(2) + 5(5) - 5^2
\][/tex]
3. Calculate each term separately:
- First term: [tex]\(4(2) = 8\)[/tex]
- Second term: [tex]\(5(5) = 25\)[/tex]
- Third term: [tex]\(5^2 = 25\)[/tex]
4. Include the sign before each term appropriately and sum them up:
[tex]\[
8 + 25 - 25
\][/tex]
5. Perform the addition and subtraction:
[tex]\[
33 - 25 = 8
\][/tex]
So, the value of the expression [tex]\(4(x-3) + 5x - x^2\)[/tex] when [tex]\(x = 5\)[/tex] is [tex]\(8\)[/tex].
