To simplify the expression [tex]\(3(x-6) + 5(x-4)\)[/tex], let's break it down step-by-step.
1. Distribute the constants inside the parentheses:
[tex]\[
3(x-6) + 5(x-4) = 3 \cdot x + 3 \cdot (-6) + 5 \cdot x + 5 \cdot (-4)
\][/tex]
[tex]\[
= 3x - 18 + 5x - 20
\][/tex]
2. Combine like terms (terms that contain [tex]\(x\)[/tex] and constant terms):
[tex]\[
3x + 5x - 18 - 20
= (3x + 5x) + (-18 - 20)
= 8x - 38
\][/tex]
Thus, the simplified expression is [tex]\(8x - 38\)[/tex].
Comparing this with the given options, the equivalent expression is:
A) [tex]\(8x - 38\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{A}
\][/tex]
