Solve for x (3-6x)/3=7x-1

$\frac{3 - 6 x}{3} = 7 x - 1$

Cancel the common factor of $3 - 6 x$ and $3$ .

Factor $3$ out of $3$ .

$\frac{3 \cdot 1 - 6 x}{3} = 7 x - 1$

Factor $3$ out of $- 6 x$ .

$\frac{3 \cdot 1 + 3 (- 2 x)}{3} = 7 x - 1$

Factor $3$ out of $3 (1) + 3 (- 2 x)$ .

$\frac{3 (1 - 2 x)}{3} = 7 x - 1$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (1 - 2 x)}{3 (1)} = 7 x - 1$

Cancel the common factor.

$\frac{3 (1 - 2 x)}{3 \cdot 1} = 7 x - 1$

Rewrite the expression.

$\frac{1 - 2 x}{1} = 7 x - 1$

Divide $1 - 2 x$ by $1$ .

$1 - 2 x = 7 x - 1$

Solve for $x$ .

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

Subtract $7 x$ from both sides of the equation.

$1 - 2 x - 7 x = - 1$

Subtract $7 x$ from $- 2 x$ .

$1 - 9 x = - 1$

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

Subtract $1$ from both sides of the equation.

$- 9 x = - 1 - 1$

Subtract $1$ from $- 1$ .

$- 9 x = - 2$

Divide each term in $- 9 x = - 2$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 2$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 2}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 2}{- 9}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 9}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{9}$

Decimal Form:

$x = 0.\overline{2}$