Solve for x 2/3(x-6)=-1/3x-14

$\frac{2}{3} (x - 6) = - \frac{1}{3} x - 14$

Simplify $\frac{2}{3} \cdot (x - 6)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (x - 6) = - \frac{1}{3} x - 14$

Simplify by adding zeros.

$\frac{2}{3} \cdot (x - 6) = - \frac{1}{3} x - 14$

Apply the distributive property.

$\frac{2}{3} x + \frac{2}{3} \cdot - 6 = - \frac{1}{3} x - 14$

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

$\frac{2 x}{3} + \frac{2}{3} \cdot - 6 = - \frac{1}{3} x - 14$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$\frac{2 x}{3} + \frac{2}{3} \cdot (3 (- 2)) = - \frac{1}{3} x - 14$

Cancel the common factor.

$\frac{2 x}{3} + \frac{2}{3} \cdot (3 \cdot - 2) = - \frac{1}{3} x - 14$

Rewrite the expression.

$\frac{2 x}{3} + 2 \cdot - 2 = - \frac{1}{3} x - 14$

Multiply $2$ by $- 2$ .

$\frac{2 x}{3} - 4 = - \frac{1}{3} x - 14$

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

$\frac{2 x}{3} - 4 = - \frac{x}{3} - 14$

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

Add $\frac{x}{3}$ to both sides of the equation.

$\frac{2 x}{3} - 4 + \frac{x}{3} = - 14$

Combine the numerators over the common denominator.

$- 4 + \frac{2 x + x}{3} = - 14$

Add $2 x$ and $x$ .

$- 4 + \frac{3 x}{3} = - 14$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 4 + \frac{3 x}{3} = - 14$

Divide $x$ by $1$ .

$- 4 + x = - 14$

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

Add $4$ to both sides of the equation.

$x = - 14 + 4$

Add $- 14$ and $4$ .

$x = - 10$