Math

Question Solve for kk given 8k+2m=3m+k8k + 2m = 3m + k with solutions k=70m,k=7m,k=7m,k=m7k = 70m, k = 7m, k = \frac{7}{\sqrt{m}}, k = \frac{m}{7}.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 8k+2m=3m+k8k + 2m = 3m + k.
2. We need to solve for kk in terms of mm.

STEP 2

First, we will collect all terms involving kk on one side of the equation and all terms involving mm on the other side. We can do this by subtracting kk and 2m2m from both sides of the equation.
8k+2mk2m=3m+kk2m8k + 2m - k - 2m = 3m + k - k - 2m

STEP 3

Simplify both sides of the equation by combining like terms.
7k=m7k = m

STEP 4

Now, we have an equation with kk on one side and mm on the other side. To solve for kk, we need to isolate kk. Since 7k=m7k = m, we can divide both sides by 7 to get kk by itself.
7k7=m7\frac{7k}{7} = \frac{m}{7}

STEP 5

Simplify both sides of the equation to find the value of kk.
k=m7k = \frac{m}{7}
Therefore, the correct answer is k=m7k = \frac{m}{7}.

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