Sure, let's break down and simplify the given mathematical expression step-by-step.
We start with the expression [tex]\(3(1 + x) + 7\)[/tex].
1. Distribute the 3 inside the parentheses:
[tex]\[
3(1 + x) + 7 = 3 \cdot 1 + 3 \cdot x + 7
\][/tex]
Simplifying the multiplication, we get:
[tex]\[
3 + 3x + 7
\][/tex]
2. Combine like terms:
- We have two constant terms, [tex]\(3\)[/tex] and [tex]\(7\)[/tex].
- Adding these constants together:
[tex]\[
3 + 7 = 10
\][/tex]
- So, the expression becomes:
[tex]\[
3x + 10
\][/tex]
Thus, the simplified expression is:
[tex]\[
3x + 10
\][/tex]
Now, let's compare this result with the given options:
- A. [tex]\(x + 7\)[/tex] - incorrect
- B. [tex]\(x + 10\)[/tex] - incorrect
- C. [tex]\(3x + 7\)[/tex] - incorrect
- D. [tex]\(3x + 10\)[/tex] - correct
Therefore, the expression equivalent to [tex]\(3(1 + x) + 7\)[/tex] is [tex]\(\boxed{D}\)[/tex].
