First, let's start by solving the given linear equation step-by-step:
The equation provided is:
[tex]\[
8k + 2m = 3m + k
\][/tex]
### Step 1: Move all terms involving [tex]\( k \)[/tex] to one side and all terms involving [tex]\( m \)[/tex] to the other side:
Subtract [tex]\( k \)[/tex] from both sides:
[tex]\[
8k - k + 2m = 3m
\][/tex]
This simplifies to:
[tex]\[
7k + 2m = 3m
\][/tex]
Next, subtract [tex]\( 2m \)[/tex] from both sides:
[tex]\[
7k = 3m - 2m
\][/tex]
This simplifies to:
[tex]\[
7k = m
\][/tex]
### Step 2: Solve for [tex]\( k \)[/tex]:
To isolate [tex]\( k \)[/tex], divide both sides of the equation by 7:
[tex]\[
k = \frac{m}{7}
\][/tex]
We have now solved for [tex]\( k \)[/tex], and the solution is:
[tex]\[
k = \frac{m}{7}
\][/tex]
Among the given options, the one that matches this result is:
[tex]\[
k = \frac{m}{7}
\][/tex]
To verify, let's rewrite the final solution set using the derived value:
- [tex]\( k = 70m \)[/tex] is not correct.
- [tex]\( k = 7m \)[/tex] is not correct.
- [tex]\( k = \frac{7}{m} \)[/tex] is not correct.
- [tex]\( k = \frac{m}{7} \)[/tex] is correct.
So, the correct answer is:
[tex]\[
k = \frac{m}{7}
\][/tex]
