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Solve for [tex]$k$[/tex].

[tex] 8k + 2m = 3m + k [/tex]

A. [tex]k = 7m[/tex]
B. [tex]k = \frac{7}{m}[/tex]
C. [tex]k = \frac{m}{7}[/tex]

Sagot :

GinnyAnsweridn
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]
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