Solve for k 1/2k+6=4k-8

$\frac{1}{2} k + 6 = 4 k - 8$

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

$\frac{k}{2} + 6 = 4 k - 8$

Move all terms containing $k$ to the left side of the equation.

Subtract $4 k$ from both sides of the equation.

$\frac{k}{2} + 6 - 4 k = - 8$

To write $- 4 k$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{k}{2} - 4 k \cdot \frac{2}{2} + 6 = - 8$

Combine $- 4 k$ and $\frac{2}{2}$ .

$\frac{k}{2} + \frac{- 4 k \cdot 2}{2} + 6 = - 8$

Combine the numerators over the common denominator.

$\frac{k - 4 k \cdot 2}{2} + 6 = - 8$

Simplify each term.

Simplify the numerator.

Factor $k$ out of $k - 4 k \cdot 2$ .

Raise $k$ to the power of $1$ .

$\frac{k^{1} - 4 k \cdot 2}{2} + 6 = - 8$

Factor $k$ out of $k^{1}$ .

$\frac{k \cdot 1 - 4 k \cdot 2}{2} + 6 = - 8$

Factor $k$ out of $- 4 k \cdot 2$ .

$\frac{k \cdot 1 + k (- 4 \cdot 2)}{2} + 6 = - 8$

Factor $k$ out of $k \cdot 1 + k (- 4 \cdot 2)$ .

$\frac{k (1 - 4 \cdot 2)}{2} + 6 = - 8$

Multiply $- 4$ by $2$ .

$\frac{k (1 - 8)}{2} + 6 = - 8$

Subtract $8$ from $1$ .

$\frac{k \cdot - 7}{2} + 6 = - 8$

Move $- 7$ to the left of $k$ .

$\frac{- 7 \cdot k}{2} + 6 = - 8$

Move the negative in front of the fraction.

$- \frac{7 k}{2} + 6 = - 8$

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

Subtract $6$ from both sides of the equation.

$- \frac{7 k}{2} = - 8 - 6$

Subtract $6$ from $- 8$ .

$- \frac{7 k}{2} = - 14$

Multiply both sides of the equation by $- \frac{2}{7}$ .

$- \frac{2}{7} (- \frac{7 k}{2}) = - \frac{2}{7} \cdot - 14$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{7} (- \frac{7 k}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$\frac{- 2}{7} (- \frac{7 k}{2}) = - \frac{2}{7} \cdot - 14$

Move the leading negative in $- \frac{7 k}{2}$ into the numerator.

$\frac{- 2}{7} \cdot \frac{- 7 k}{2} = - \frac{2}{7} \cdot - 14$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{7} \cdot \frac{- 7 k}{2} = - \frac{2}{7} \cdot - 14$

Cancel the common factor.

$\frac{2 \cdot - 1}{7} \cdot \frac{- 7 k}{2} = - \frac{2}{7} \cdot - 14$

Rewrite the expression.

$\frac{- 1}{7} (- 7 k) = - \frac{2}{7} \cdot - 14$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 k$ .

$\frac{- 1}{7} (7 (- k)) = - \frac{2}{7} \cdot - 14$

Cancel the common factor.

$\frac{- 1}{7} (7 (- k)) = - \frac{2}{7} \cdot - 14$

Rewrite the expression.

$- - k = - \frac{2}{7} \cdot - 14$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k = - \frac{2}{7} \cdot - 14$

Multiply $k$ by $1$ .

$k = - \frac{2}{7} \cdot - 14$

Simplify the right side.

Simplify $- \frac{2}{7} \cdot - 14$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{2}{7}$ into the numerator.

$k = \frac{- 2}{7} \cdot - 14$

Factor $7$ out of $- 14$ .

$k = \frac{- 2}{7} \cdot (7 (- 2))$

Cancel the common factor.

$k = \frac{- 2}{7} \cdot (7 \cdot - 2)$

Rewrite the expression.

$k = - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$k = 4$

Solve for k 1/2k+6=4k-8

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