Solve for v 5/14v-3/7=2/7

$\frac{5}{14} v - \frac{3}{7} = \frac{2}{7}$

Step 1

Combine $\frac{5}{14}$ and $v$ .

$\frac{5 v}{14} - \frac{3}{7} = \frac{2}{7}$

Step 2

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

Add $\frac{3}{7}$ to both sides of the equation.

$\frac{5 v}{14} = \frac{2}{7} + \frac{3}{7}$

Combine the numerators over the common denominator.

$\frac{5 v}{14} = \frac{2 + 3}{7}$

Add $2$ and $3$ .

$\frac{5 v}{14} = \frac{5}{7}$

Step 3

Multiply both sides of the equation by $\frac{14}{5}$ .

$\frac{14}{5} \cdot \frac{5 v}{14} = \frac{14}{5} \cdot \frac{5}{7}$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{14}{5} \cdot \frac{5 v}{14}$ .

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14}{5} \cdot \frac{5 v}{14} = \frac{14}{5} \cdot \frac{5}{7}$

Rewrite the expression.

$\frac{1}{5} (5 v) = \frac{14}{5} \cdot \frac{5}{7}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 v$ .

$\frac{1}{5} (5 (v)) = \frac{14}{5} \cdot \frac{5}{7}$

Cancel the common factor.

$\frac{1}{5} (5 v) = \frac{14}{5} \cdot \frac{5}{7}$

Rewrite the expression.

$v = \frac{14}{5} \cdot \frac{5}{7}$

Simplify the right side.

Simplify $\frac{14}{5} \cdot \frac{5}{7}$ .

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$v = \frac{7 (2)}{5} \cdot \frac{5}{7}$

Cancel the common factor.

$v = \frac{7 \cdot 2}{5} \cdot \frac{5}{7}$

Rewrite the expression.

$v = \frac{2}{5} \cdot 5$

Cancel the common factor of $5$ .

Cancel the common factor.

$v = \frac{2}{5} \cdot 5$

Rewrite the expression.

$v = 2$