Solve for x 3/7=(x-2)/6

$\frac{3}{7} = \frac{x - 2}{6}$

Rewrite the equation as $\frac{x - 2}{6} = \frac{3}{7}$ .

$\frac{x - 2}{6} = \frac{3}{7}$

Multiply both sides of the equation by $6$ .

$6 \frac{x - 2}{6} = 6 (\frac{3}{7})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{x - 2}{6} = 6 (\frac{3}{7})$

Rewrite the expression.

$x - 2 = 6 (\frac{3}{7})$

Simplify the right side.

Multiply $6 (\frac{3}{7})$ .

Combine $6$ and $\frac{3}{7}$ .

$x - 2 = \frac{6 \cdot 3}{7}$

Multiply $6$ by $3$ .

$x - 2 = \frac{18}{7}$

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

Add $2$ to both sides of the equation.

$x = \frac{18}{7} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = \frac{18}{7} + 2 \cdot \frac{7}{7}$

Combine $2$ and $\frac{7}{7}$ .

$x = \frac{18}{7} + \frac{2 \cdot 7}{7}$

Combine the numerators over the common denominator.

$x = \frac{18 + 2 \cdot 7}{7}$

Simplify the numerator.

Multiply $2$ by $7$ .

$x = \frac{18 + 14}{7}$

Add $18$ and $14$ .

$x = \frac{32}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{32}{7}$

Decimal Form:

$x = 4.\overline{571428}$

Mixed Number Form:

$x = 4 \frac{4}{7}$