Solve for x 1/3(x+6)=2/3(x-9)

$\frac{1}{3} (x + 6) = \frac{2}{3} (x - 9)$

Step 1

Simplify $\frac{1}{3} \cdot (x + 6)$ .

Start simplifying.

$0 + 0 + \frac{1}{3} \cdot (x + 6) = \frac{2}{3} \cdot (x - 9)$

Simplify by adding zeros.

$\frac{1}{3} \cdot (x + 6) = \frac{2}{3} \cdot (x - 9)$

Apply the distributive property.

$\frac{1}{3} x + \frac{1}{3} \cdot 6 = \frac{2}{3} \cdot (x - 9)$

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

$\frac{x}{3} + \frac{1}{3} \cdot 6 = \frac{2}{3} \cdot (x - 9)$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

Apply the distributive property.

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

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $- 3$ .

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

Step 3

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

Subtract $\frac{2 x}{3}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $2 x$ from $x$ .

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

Move the negative in front of the fraction.

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

Step 4

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $- 6$ .

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

Step 5

Multiply both sides of the equation by $- 3$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 \cdot - 8$

Rewrite the expression.

$- - x = - 3 \cdot - 8$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 8$

Multiply $x$ by $1$ .

$x = - 3 \cdot - 8$

Simplify the right side.

Multiply $- 3$ by $- 8$ .

$x = 24$

Solve for x 1/3(x+6)=2/3(x-9)

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