Let's solve the equation [tex]\( 2x - 8y = 12 \)[/tex] for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex] step by step.
1. Starting with the given equation:
[tex]\[
2x - 8y = 12
\][/tex]
2. Isolate the [tex]\( x \)[/tex]-term on one side of the equation.
To do this, we can add [tex]\( 8y \)[/tex] to both sides of the equation to remove the [tex]\( -8y \)[/tex] term from the left side. This is done to move [tex]\( y \)[/tex] to the right side:
[tex]\[
2x = 8y + 12
\][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by the coefficient of [tex]\( x \)[/tex].
The coefficient of [tex]\( x \)[/tex] is [tex]\( 2 \)[/tex], so we divide both sides by [tex]\( 2 \)[/tex]:
[tex]\[
x = \frac{8y + 12}{2}
\][/tex]
4. Simplify the right side of the equation.
Divide each term in the numerator by [tex]\( 2 \)[/tex]:
[tex]\[
x = \frac{8y}{2} + \frac{12}{2}
\][/tex]
Simplifying further, we get:
[tex]\[
x = 4y + 6
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{x = 4y + 6}
\][/tex]
So, the answer is B. [tex]\( x = 4y + 6 \)[/tex].
