Solve for k k/3+4-2k=-9k

$\frac{k}{3} + 4 - 2 k = - 9 k$

Simplify $\frac{k}{3} + 4 - 2 k$ .

To write $- 2 k$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{k}{3} - 2 k \cdot \frac{3}{3} + 4 = - 9 k$

Simplify terms.

Combine $- 2 k$ and $\frac{3}{3}$ .

$\frac{k}{3} + \frac{- 2 k \cdot 3}{3} + 4 = - 9 k$

Combine the numerators over the common denominator.

$\frac{k - 2 k \cdot 3}{3} + 4 = - 9 k$

Simplify each term.

Simplify the numerator.

Factor $k$ out of $k - 2 k \cdot 3$ .

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

$\frac{k^{1} - 2 k \cdot 3}{3} + 4 = - 9 k$

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

$\frac{k \cdot 1 - 2 k \cdot 3}{3} + 4 = - 9 k$

Factor $k$ out of $- 2 k \cdot 3$ .

$\frac{k \cdot 1 + k (- 2 \cdot 3)}{3} + 4 = - 9 k$

Factor $k$ out of $k \cdot 1 + k (- 2 \cdot 3)$ .

$\frac{k (1 - 2 \cdot 3)}{3} + 4 = - 9 k$

Multiply $- 2$ by $3$ .

$\frac{k (1 - 6)}{3} + 4 = - 9 k$

Subtract $6$ from $1$ .

$\frac{k \cdot - 5}{3} + 4 = - 9 k$

Move $- 5$ to the left of $k$ .

$\frac{- 5 \cdot k}{3} + 4 = - 9 k$

Move the negative in front of the fraction.

$- \frac{5 k}{3} + 4 = - 9 k$

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

Add $9 k$ to both sides of the equation.

$- \frac{5 k}{3} + 4 + 9 k = 0$

To write $9 k$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{5 k}{3} + 9 k \cdot \frac{3}{3} + 4 = 0$

Combine $9 k$ and $\frac{3}{3}$ .

$- \frac{5 k}{3} + \frac{9 k \cdot 3}{3} + 4 = 0$

Combine the numerators over the common denominator.

$\frac{- 5 k + 9 k \cdot 3}{3} + 4 = 0$

Simplify each term.

Simplify the numerator.

Factor $k$ out of $- 5 k + 9 k \cdot 3$ .

Factor $k$ out of $- 5 k$ .

$\frac{k \cdot - 5 + 9 k \cdot 3}{3} + 4 = 0$

Factor $k$ out of $9 k \cdot 3$ .

$\frac{k \cdot - 5 + k (9 \cdot 3)}{3} + 4 = 0$

Factor $k$ out of $k \cdot - 5 + k (9 \cdot 3)$ .

$\frac{k (- 5 + 9 \cdot 3)}{3} + 4 = 0$

Multiply $9$ by $3$ .

$\frac{k (- 5 + 27)}{3} + 4 = 0$

Add $- 5$ and $27$ .

$\frac{k \cdot 22}{3} + 4 = 0$

Move $22$ to the left of $k$ .

$\frac{22 k}{3} + 4 = 0$

Subtract $4$ from both sides of the equation.

$\frac{22 k}{3} = - 4$

Multiply both sides of the equation by $\frac{3}{22}$ .

$\frac{3}{22} \cdot \frac{22 k}{3} = \frac{3}{22} \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{22} \cdot \frac{22 k}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{22} \cdot \frac{22 k}{3} = \frac{3}{22} \cdot - 4$

Rewrite the expression.

$\frac{1}{22} (22 k) = \frac{3}{22} \cdot - 4$

Cancel the common factor of $22$ .

Factor $22$ out of $22 k$ .

$\frac{1}{22} (22 (k)) = \frac{3}{22} \cdot - 4$

Cancel the common factor.

$\frac{1}{22} (22 k) = \frac{3}{22} \cdot - 4$

Rewrite the expression.

$k = \frac{3}{22} \cdot - 4$

Simplify the right side.

Simplify $\frac{3}{22} \cdot - 4$ .

Cancel the common factor of $2$ .

Factor $2$ out of $22$ .

$k = \frac{3}{2 (11)} \cdot - 4$

Factor $2$ out of $- 4$ .

$k = \frac{3}{2 \cdot 11} \cdot (2 \cdot - 2)$

Cancel the common factor.

$k = \frac{3}{2 \cdot 11} \cdot (2 \cdot - 2)$

Rewrite the expression.

$k = \frac{3}{11} \cdot - 2$

Combine $\frac{3}{11}$ and $- 2$ .

$k = \frac{3 \cdot - 2}{11}$

Simplify the expression.

Multiply $3$ by $- 2$ .

$k = \frac{- 6}{11}$

Move the negative in front of the fraction.

$k = - \frac{6}{11}$

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{6}{11}$

Decimal Form:

$k = - 0.\overline{54}$

Solve for k k/3+4-2k=-9k

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