To solve the equation [tex]\( 6x - 12y = 18 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Isolate the term containing [tex]\( x \)[/tex]:
[tex]\[
6x - 12y = 18
\][/tex]
Add [tex]\( 12y \)[/tex] to both sides of the equation to move the term involving [tex]\( y \)[/tex] to the right side:
[tex]\[
6x = 12y + 18
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 6:
[tex]\[
x = \frac{12y + 18}{6}
\][/tex]
3. Simplify the equation:
Break down the fraction on the right side by distributing the division by 6:
[tex]\[
x = \frac{12y}{6} + \frac{18}{6}
\][/tex]
Simplify the terms:
[tex]\[
x = 2y + 3
\][/tex]
Thus, the solution to the equation [tex]\( 6x - 12y = 18 \)[/tex] for [tex]\( x \)[/tex] is:
[tex]\[
x = 2y + 3
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{B}
\][/tex]
