To solve the equation [tex]\(30 k x - 6 k x = 8\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Combine like terms on the left side of the equation:
The left side of the equation has two terms that both contain the variable [tex]\(k x\)[/tex]. So, we can combine these terms:
[tex]\[
30 k x - 6 k x = 8
\][/tex]
Subtract [tex]\(6 k x\)[/tex] from [tex]\(30 k x\)[/tex]:
[tex]\[
(30 k - 6 k)x = 8
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
24 k x = 8
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we need to isolate it on one side of the equation. Divide both sides of the equation by [tex]\(24 k\)[/tex]:
[tex]\[
x = \frac{8}{24 k}
\][/tex]
4. Simplify the fraction:
Simplify [tex]\(\frac{8}{24}\)[/tex]:
[tex]\[
x = \frac{1}{3 k}
\][/tex]
So, the solution to the equation [tex]\(30 k x - 6 k x = 8\)[/tex] for [tex]\(x\)[/tex] is:
[tex]\[
x = \frac{1}{3 k}
\][/tex]
The correct option is B. [tex]\(x = \frac{1}{3 k}\)[/tex].
