Solve for k 1/4k+1/2(1/2k+4)=6

$\frac{1}{4} k + \frac{1}{2} (\frac{1}{2} k + 4) = 6$

Step 1

Simplify $\frac{1}{4} k + \frac{1}{2} \cdot (\frac{1}{2} k + 4)$ .

Simplify each term.

Combine $\frac{1}{4}$ and $k$ .

$\frac{k}{4} + \frac{1}{2} \cdot (\frac{1}{2} k + 4) = 6$

Combine $\frac{1}{2}$ and $k$ .

$\frac{k}{4} + \frac{1}{2} \cdot (\frac{k}{2} + 4) = 6$

Apply the distributive property.

$\frac{k}{4} + \frac{1}{2} \cdot \frac{k}{2} + \frac{1}{2} \cdot 4 = 6$

Multiply $\frac{1}{2} \cdot \frac{k}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{k}{2}$ .

$\frac{k}{4} + \frac{k}{2 \cdot 2} + \frac{1}{2} \cdot 4 = 6$

Multiply $2$ by $2$ .

$\frac{k}{4} + \frac{k}{4} + \frac{1}{2} \cdot 4 = 6$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{k}{4} + \frac{k}{4} + \frac{1}{2} \cdot (2 (2)) = 6$

Cancel the common factor.

$\frac{k}{4} + \frac{k}{4} + \frac{1}{2} \cdot (2 \cdot 2) = 6$

Rewrite the expression.

$\frac{k}{4} + \frac{k}{4} + 2 = 6$

Simplify terms.

Combine the numerators over the common denominator.

$2 + \frac{k + k}{4} = 6$

Add $k$ and $k$ .

$2 + \frac{2 k}{4} = 6$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 k$ .

$2 + \frac{2 (k)}{4} = 6$

Cancel the common factors.

Factor $2$ out of $4$ .

$2 + \frac{2 k}{2 \cdot 2} = 6$

Cancel the common factor.

$2 + \frac{2 k}{2 \cdot 2} = 6$

Rewrite the expression.

$2 + \frac{k}{2} = 6$

Step 2

Move all terms not containing $k$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\frac{k}{2} = 6 - 2$

Subtract $2$ from $6$ .

$\frac{k}{2} = 4$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{k}{2} = 2 \cdot 4$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{k}{2} = 2 \cdot 4$

Rewrite the expression.

$k = 2 \cdot 4$

Simplify the right side.

Multiply $2$ by $4$ .

$k = 8$

Solve for k 1/4k+1/2(1/2k+4)=6

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