Solve for [tex]\( x \)[/tex]:

[tex]\[ 6x - 12y = 18 \][/tex]

A. [tex]\( x = 2y + 18 \)[/tex]

B. [tex]\( x = 2y + 3 \)[/tex]

C. [tex]\( x = 12y + 18 \)[/tex]

D. [tex]\( x = 12y + 3 \)[/tex]



Answer :

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]