Sure, let's solve for [tex]\( k \)[/tex] in the given equation:
[tex]\[ 8k + 2m = 3m + k \][/tex]
We'll start by simplifying the equation step-by-step.
1. First, isolate all [tex]\( k \)[/tex] terms on one side of the equation and all [tex]\( m \)[/tex] terms on the other side. Subtract [tex]\( k \)[/tex] from both sides:
[tex]\[ 8k + 2m - k = 3m + k - k \][/tex]
2. This simplifies to:
[tex]\[ 7k + 2m = 3m \][/tex]
3. Next, subtract [tex]\( 2m \)[/tex] from both sides to isolate the [tex]\( k \)[/tex] terms:
[tex]\[ 7k + 2m - 2m = 3m - 2m \][/tex]
4. This simplifies to:
[tex]\[ 7k = m \][/tex]
5. To solve for [tex]\( k \)[/tex], divide both sides of the equation by 7:
[tex]\[ k = \frac{m}{7} \][/tex]
Now we have the solution for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{m}{7} \][/tex]
Therefore, among the given choices:
- [tex]\( k = 70m \)[/tex]
- [tex]\( k = 7m \)[/tex]
- [tex]\( k = \frac{7}{m} \)[/tex]
- [tex]\( k = \frac{m}{7} \)[/tex]
The correct answer is:
[tex]\[ k = \frac{m}{7} \][/tex]
