Solve for v 2/3v-6=6-2/3v

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

Step 1

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

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

Step 2

Simplify each term.

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

$\frac{2 v}{3} - 6 = 6 - \frac{v \cdot 2}{3}$

Move $2$ to the left of $v$ .

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

Step 3

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

Add $\frac{2 v}{3}$ to both sides of the equation.

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

Combine the numerators over the common denominator.

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

Add $2 v$ and $2 v$ .

$- 6 + \frac{4 v}{3} = 6$

Step 4

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

Add $6$ to both sides of the equation.

$\frac{4 v}{3} = 6 + 6$

Add $6$ and $6$ .

$\frac{4 v}{3} = 12$

Step 5

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 v}{3} = \frac{3}{4} \cdot 12$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{4} \cdot \frac{4 v}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 v}{3} = \frac{3}{4} \cdot 12$

Rewrite the expression.

$\frac{1}{4} (4 v) = \frac{3}{4} \cdot 12$

Cancel the common factor of $4$ .

Factor $4$ out of $4 v$ .

$\frac{1}{4} (4 (v)) = \frac{3}{4} \cdot 12$

Cancel the common factor.

$\frac{1}{4} (4 v) = \frac{3}{4} \cdot 12$

Rewrite the expression.

$v = \frac{3}{4} \cdot 12$

Simplify the right side.

Simplify $\frac{3}{4} \cdot 12$ .

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$v = \frac{3}{4} \cdot (4 (3))$

Cancel the common factor.

$v = \frac{3}{4} \cdot (4 \cdot 3)$

Rewrite the expression.

$v = 3 \cdot 3$

Multiply $3$ by $3$ .

$v = 9$

Solve for v 2/3v-6=6-2/3v

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