To solve the equation [tex]\(11 k x + 13 k x = 6\)[/tex] for [tex]\(x\)[/tex], let's follow a step-by-step approach.
1. Combine like terms:
Start by combining the terms on the left-hand side of the equation. Both terms contain [tex]\(k\)[/tex] and [tex]\(x\)[/tex], so we can factor these out:
[tex]\[
11 k x + 13 k x = (11 + 13) k x = 24 k x
\][/tex]
This simplifies our equation to:
[tex]\[
24 k x = 6
\][/tex]
2. Isolate [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by [tex]\(24 k\)[/tex]:
[tex]\[
24 k x = 6 \implies x = \frac{6}{24 k}
\][/tex]
3. Simplify the fraction:
Simplify the fraction [tex]\(\frac{6}{24 k}\)[/tex]:
[tex]\[
x = \frac{6}{24 k} = \frac{1}{4 k}
\][/tex]
Thus, the solution for [tex]\(x\)[/tex] is:
[tex]\[
x = \frac{1}{4 k}
\][/tex]
So, the correct answer is:
A. [tex]\(x = \frac{1}{4 k}\)[/tex]
