Solve for k 2/3(1/2k-9)=3/2(4+2k)

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

Simplify $\frac{2}{3} \cdot (\frac{1}{2} k - 9)$ .

Start simplifying.

$0 + 0 + \frac{2}{3} \cdot (\frac{1}{2} k - 9) = \frac{3}{2} \cdot (4 + 2 k)$

Simplify by adding zeros.

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{1}{3}$ and $k$ .

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 3$ .

$\frac{k}{3} - 6 = \frac{3}{2} \cdot (4 + 2 k)$

Simplify $\frac{3}{2} \cdot (4 + 2 k)$ .

Apply the distributive property.

$\frac{k}{3} - 6 = \frac{3}{2} \cdot 4 + \frac{3}{2} (2 k)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{k}{3} - 6 = \frac{3}{2} \cdot (2 (2)) + \frac{3}{2} (2 k)$

Cancel the common factor.

$\frac{k}{3} - 6 = \frac{3}{2} \cdot (2 \cdot 2) + \frac{3}{2} (2 k)$

Rewrite the expression.

$\frac{k}{3} - 6 = 3 \cdot 2 + \frac{3}{2} (2 k)$

Multiply $3$ by $2$ .

$\frac{k}{3} - 6 = 6 + \frac{3}{2} (2 k)$

Cancel the common factor of $2$ .

Factor $2$ out of $2 k$ .

$\frac{k}{3} - 6 = 6 + \frac{3}{2} (2 (k))$

Cancel the common factor.

$\frac{k}{3} - 6 = 6 + \frac{3}{2} (2 k)$

Rewrite the expression.

$\frac{k}{3} - 6 = 6 + 3 k$

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

Subtract $3 k$ from both sides of the equation.

$\frac{k}{3} - 6 - 3 k = 6$

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

$\frac{k}{3} - 3 k \cdot \frac{3}{3} - 6 = 6$

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

$\frac{k}{3} + \frac{- 3 k \cdot 3}{3} - 6 = 6$

Combine the numerators over the common denominator.

$\frac{k - 3 k \cdot 3}{3} - 6 = 6$

Simplify each term.

Simplify the numerator.

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

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

$\frac{k^{1} - 3 k \cdot 3}{3} - 6 = 6$

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

$\frac{k \cdot 1 - 3 k \cdot 3}{3} - 6 = 6$

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

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

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

$\frac{k (1 - 3 \cdot 3)}{3} - 6 = 6$

Multiply $- 3$ by $3$ .

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

Subtract $9$ from $1$ .

$\frac{k \cdot - 8}{3} - 6 = 6$

Move $- 8$ to the left of $k$ .

$\frac{- 8 \cdot k}{3} - 6 = 6$

Move the negative in front of the fraction.

$- \frac{8 k}{3} - 6 = 6$

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

Add $6$ to both sides of the equation.

$- \frac{8 k}{3} = 6 + 6$

Add $6$ and $6$ .

$- \frac{8 k}{3} = 12$

Multiply both sides of the equation by $- \frac{3}{8}$ .

$- \frac{3}{8} (- \frac{8 k}{3}) = - \frac{3}{8} \cdot 12$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{8} (- \frac{8 k}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{- 3}{8} (- \frac{8 k}{3}) = - \frac{3}{8} \cdot 12$

Move the leading negative in $- \frac{8 k}{3}$ into the numerator.

$\frac{- 3}{8} \cdot \frac{- 8 k}{3} = - \frac{3}{8} \cdot 12$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{8} \cdot \frac{- 8 k}{3} = - \frac{3}{8} \cdot 12$

Cancel the common factor.

$\frac{3 \cdot - 1}{8} \cdot \frac{- 8 k}{3} = - \frac{3}{8} \cdot 12$

Rewrite the expression.

$\frac{- 1}{8} (- 8 k) = - \frac{3}{8} \cdot 12$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8 k$ .

$\frac{- 1}{8} (8 (- k)) = - \frac{3}{8} \cdot 12$

Cancel the common factor.

$\frac{- 1}{8} (8 (- k)) = - \frac{3}{8} \cdot 12$

Rewrite the expression.

$- - k = - \frac{3}{8} \cdot 12$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 k = - \frac{3}{8} \cdot 12$

Multiply $k$ by $1$ .

$k = - \frac{3}{8} \cdot 12$

Simplify the right side.

Simplify $- \frac{3}{8} \cdot 12$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$k = \frac{- 3}{8} \cdot 12$

Factor $4$ out of $8$ .

$k = \frac{- 3}{4 (2)} \cdot 12$

Factor $4$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify the expression.

Multiply $- 3$ by $3$ .

$k = \frac{- 9}{2}$

Move the negative in front of the fraction.

$k = - \frac{9}{2}$

The result can be shown in multiple forms.

Exact Form:

$k = - \frac{9}{2}$

Decimal Form:

$k = - 4.5$

Mixed Number Form:

$k = - 4 \frac{1}{2}$

Solve for k 2/3(1/2k-9)=3/2(4+2k)

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