To determine which expression is equivalent to [tex]\(3(x-6) + 5(x-4)\)[/tex], we need to simplify the given expression step-by-step.
Let's start by expanding the expression:
1. Distribute the constants inside the parentheses:
[tex]\[
3(x - 6) = 3x - 18
\][/tex]
[tex]\[
5(x - 4) = 5x - 20
\][/tex]
2. Next, add the results from step 1 together:
[tex]\[
3x - 18 + 5x - 20
\][/tex]
3. Combine like terms (the terms that contain [tex]\(x\)[/tex] and the constant terms):
- Combine the [tex]\(x\)[/tex]-terms: [tex]\(3x + 5x = 8x\)[/tex]
- Combine the constant terms: [tex]\(-18 - 20 = -38\)[/tex]
So, the simplified expression is:
[tex]\[
8x - 38
\][/tex]
Comparing this with the given answer choices, we find that the equivalent expression is:
B) [tex]\(8x - 38\)[/tex]
Therefore, the expression [tex]\(3(x-6) + 5(x-4)\)[/tex] simplifies to [tex]\(8x - 38\)[/tex].
