Let's solve the equation step-by-step.
Given equation:
[tex]\[ 6(x - 3) = 3x + 9 \][/tex]
First, distribute the 6 on the left side of the equation:
[tex]\[ 6 \cdot (x - 3) = 6x - 18 \][/tex]
Now the equation becomes:
[tex]\[ 6x - 18 = 3x + 9 \][/tex]
Next, we move the [tex]\(3x\)[/tex] from the right side to the left side by subtracting [tex]\(3x\)[/tex] from both sides:
[tex]\[ 6x - 3x - 18 = 9 \][/tex]
Simplify the equation:
[tex]\[ 3x - 18 = 9 \][/tex]
Now, we move the [tex]\(-18\)[/tex] from the left side to the right side by adding 18 to both sides:
[tex]\[ 3x = 9 + 18 \][/tex]
Simplify the right side:
[tex]\[ 3x = 27 \][/tex]
Finally, we divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{27}{3} \][/tex]
Simplify:
[tex]\[ x = 9 \][/tex]
Therefore, the solution to the equation is:
[tex]\[ \boxed{x = 9} \][/tex]
So, the correct answer is:
[tex]\[ C. \ x = 9 \][/tex]
