Solve for x 2/3-x+1/6=6x

$\frac{2}{3} - x + \frac{1}{6} = 6 x$

Simplify $\frac{2}{3} - x + \frac{1}{6}$ .

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

$- x + \frac{2}{3} \cdot \frac{2}{2} + \frac{1}{6} = 6 x$

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

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

$- x + \frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{6} = 6 x$

Multiply $3$ by $2$ .

$- x + \frac{2 \cdot 2}{6} + \frac{1}{6} = 6 x$

Combine the numerators over the common denominator.

$- x + \frac{2 \cdot 2 + 1}{6} = 6 x$

Simplify the numerator.

Multiply $2$ by $2$ .

$- x + \frac{4 + 1}{6} = 6 x$

Add $4$ and $1$ .

$- x + \frac{5}{6} = 6 x$

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

Subtract $6 x$ from both sides of the equation.

$- x + \frac{5}{6} - 6 x = 0$

Subtract $6 x$ from $- x$ .

$- 7 x + \frac{5}{6} = 0$

Subtract $\frac{5}{6}$ from both sides of the equation.

$- 7 x = - \frac{5}{6}$

Divide each term in $- 7 x = - \frac{5}{6}$ by $- 7$ and simplify.

Divide each term in $- 7 x = - \frac{5}{6}$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- \frac{5}{6}}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- \frac{5}{6}}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- \frac{5}{6}}{- 7}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5}{6} \cdot \frac{1}{- 7}$

Move the negative in front of the fraction.

$x = - \frac{5}{6} (- \frac{1}{7})$

Multiply $- \frac{5}{6} (- \frac{1}{7})$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{5}{6}) \frac{1}{7}$

Multiply $\frac{5}{6}$ by $1$ .

$x = \frac{5}{6} \cdot \frac{1}{7}$

Multiply $\frac{5}{6}$ by $\frac{1}{7}$ .

$x = \frac{5}{6 \cdot 7}$

Multiply $6$ by $7$ .

$x = \frac{5}{42}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{42}$

Decimal Form:

$x = 0.1\overline{190476}$

Solve for x 2/3-x+1/6=6x

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