Let's solve the equation step-by-step.
The given equation is:
[tex]\[ 4x + 2(x + 6) = 36 \][/tex]
1. Distribute the 2 inside the parentheses:
[tex]\[ 4x + 2(x + 6) = 4x + 2x + 12 \][/tex]
2. Combine like terms (i.e., the terms involving [tex]\(x\)[/tex]):
[tex]\[ 4x + 2x + 12 = 6x + 12 \][/tex]
3. Rewrite the equation:
[tex]\[ 6x + 12 = 36 \][/tex]
4. Subtract 12 from both sides to isolate the term containing [tex]\(x\)[/tex]:
[tex]\[ 6x + 12 - 12 = 36 - 12 \][/tex]
[tex]\[ 6x = 24 \][/tex]
5. Divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{24}{6} \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = 4 \][/tex]
Hence, the correct answer is [tex]\( \boxed{4} \)[/tex], corresponding to option D.
