Solve for v 1/2v+8=3-1/3v

$\frac{1}{2} v + 8 = 3 - \frac{1}{3} v$

Step 1

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

$\frac{v}{2} + 8 = 3 - \frac{1}{3} v$

Step 2

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

$\frac{v}{2} + 8 = 3 - \frac{v}{3}$

Step 3

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

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

$\frac{v}{2} + 8 + \frac{v}{3} = 3$

To write $\frac{v}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{v}{2} \cdot \frac{3}{3} + \frac{v}{3} + 8 = 3$

To write $\frac{v}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{v}{2} \cdot \frac{3}{3} + \frac{v}{3} \cdot \frac{2}{2} + 8 = 3$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{v}{2}$ by $\frac{3}{3}$ .

$\frac{v \cdot 3}{2 \cdot 3} + \frac{v}{3} \cdot \frac{2}{2} + 8 = 3$

Multiply $2$ by $3$ .

$\frac{v \cdot 3}{6} + \frac{v}{3} \cdot \frac{2}{2} + 8 = 3$

Multiply $\frac{v}{3}$ by $\frac{2}{2}$ .

$\frac{v \cdot 3}{6} + \frac{v \cdot 2}{3 \cdot 2} + 8 = 3$

Multiply $3$ by $2$ .

$\frac{v \cdot 3}{6} + \frac{v \cdot 2}{6} + 8 = 3$

Combine the numerators over the common denominator.

$\frac{v \cdot 3 + v \cdot 2}{6} + 8 = 3$

Reorder $v$ and $2$ .

$\frac{3 \cdot v + 2 \cdot v}{6} + 8 = 3$

Add $3 \cdot v$ and $2 \cdot v$ .

$\frac{5 v}{6} + 8 = 3$

Step 4

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

Subtract $8$ from both sides of the equation.

$\frac{5 v}{6} = 3 - 8$

Subtract $8$ from $3$ .

$\frac{5 v}{6} = - 5$

Step 5

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 v}{6} = \frac{6}{5} \cdot - 5$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 v}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 v}{6} = \frac{6}{5} \cdot - 5$

Rewrite the expression.

$\frac{1}{5} (5 v) = \frac{6}{5} \cdot - 5$

Cancel the common factor of $5$ .

Factor $5$ out of $5 v$ .

$\frac{1}{5} (5 (v)) = \frac{6}{5} \cdot - 5$

Cancel the common factor.

$\frac{1}{5} (5 v) = \frac{6}{5} \cdot - 5$

Rewrite the expression.

$v = \frac{6}{5} \cdot - 5$

Simplify the right side.

Simplify $\frac{6}{5} \cdot - 5$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$v = \frac{6}{5} \cdot (5 (- 1))$

Cancel the common factor.

$v = \frac{6}{5} \cdot (5 \cdot - 1)$

Rewrite the expression.

$v = 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$v = - 6$

Solve for v 1/2v+8=3-1/3v

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