Let's simplify the given algebraic expression step-by-step:
Given expression:
[tex]\[ 7x - 5(x + 6) \][/tex]
1. Distribute the [tex]\(-5\)[/tex] through [tex]\((x + 6)\)[/tex]:
[tex]\[ 7x - 5 \cdot x - 5 \cdot 6 \][/tex]
2. Perform the multiplication:
[tex]\[ 7x - 5x - 30 \][/tex]
3. Combine like terms ([tex]\(7x - 5x\)[/tex]):
[tex]\[ (7 - 5)x - 30 \][/tex]
[tex]\[ 2x - 30 \][/tex]
So, the simplified expression is:
[tex]\[ 2x - 30 \][/tex]
Now, let's compare this simplified expression with the given choices:
A. [tex]\(2x + 1\)[/tex]
B. [tex]\(2x + 11\)[/tex]
C. [tex]\(2x - 30\)[/tex]
D. [tex]\(2x - 1\)[/tex]
The simplified expression [tex]\(2x - 30\)[/tex] matches choice C.
Therefore, the correct answer is:
[tex]\[ \boxed{C} \][/tex]
