Solve for x (2x+4)/3=x/6-3

$\frac{2 x + 4}{3} = \frac{x}{6} - 3$

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Simplify $\frac{2 x + 4}{3} \cdot 3$ .

Factor $2$ out of $2 x + 4$ .

Factor $2$ out of $2 x$ .

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

Factor $2$ out of $4$ .

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

Factor $2$ out of $2 x + 2 \cdot 2$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Multiply $2$ by $2$ .

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

Simplify the right side.

Simplify $(\frac{x}{6} - 3) \cdot 3$ .

Apply the distributive property.

$2 x + 4 = \frac{x}{6} \cdot 3 - 3 \cdot 3$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 3$ by $3$ .

$2 x + 4 = \frac{x}{2} - 9$

Solve for $x$ .

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$2 x + 4 - \frac{x}{2} = - 9$

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

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

Combine $2 x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $2 x \cdot 2 - x$ .

Factor $x$ out of $2 x \cdot 2$ .

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

Factor $x$ out of $- x$ .

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

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

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

Multiply $2$ by $2$ .

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

Subtract $1$ from $4$ .

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

Move $3$ to the left of $x$ .

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

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

Subtract $4$ from both sides of the equation.

$\frac{3 x}{2} = - 9 - 4$

Subtract $4$ from $- 9$ .

$\frac{3 x}{2} = - 13$

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot - 13$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot - 13$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot - 13$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot - 13$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot - 13$

Rewrite the expression.

$x = \frac{2}{3} \cdot - 13$

Simplify the right side.

Simplify $\frac{2}{3} \cdot - 13$ .

Multiply $\frac{2}{3} \cdot - 13$ .

Combine $\frac{2}{3}$ and $- 13$ .

$x = \frac{2 \cdot - 13}{3}$

Multiply $2$ by $- 13$ .

$x = \frac{- 26}{3}$

Move the negative in front of the fraction.

$x = - \frac{26}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{26}{3}$

Decimal Form:

$x = - 8.\overline{6}$

Mixed Number Form:

$x = - 8 \frac{2}{3}$

Solve for x (2x+4)/3=x/6-3

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