Certainly! Let's evaluate the expression [tex]\( 3(3x + y) - 5x + 13 \)[/tex] step by step for the given values of [tex]\( x = 4 \)[/tex] and [tex]\( y = 7 \)[/tex].
1. Substitute the given values into the expression:
[tex]\[
x = 4, \quad y = 7
\][/tex]
The expression becomes:
[tex]\[
3(3(4) + 7) - 5(4) + 13
\][/tex]
2. Simplify inside the parentheses:
First, calculate [tex]\(3(4)\)[/tex]:
[tex]\[
3(4) = 12
\][/tex]
Then add [tex]\(y\)[/tex] (which is 7) to this product:
[tex]\[
12 + 7 = 19
\][/tex]
3. Multiply the result by 3:
[tex]\[
3(19) = 57
\][/tex]
4. Subtract [tex]\(5x\)[/tex] where [tex]\(x = 4\)[/tex]:
Calculate [tex]\(5(4)\)[/tex]:
[tex]\[
5(4) = 20
\][/tex]
Then subtract this result from 57:
[tex]\[
57 - 20 = 37
\][/tex]
5. Finally, add 13:
[tex]\[
37 + 13 = 50
\][/tex]
Therefore, the expression evaluates to:
[tex]\[
3(3x + y) - 5x + 13 = 50
\][/tex]
So, the answer is:
[tex]\[
50
\][/tex]
