Solve for x -1/6x-5=2/3x

$- \frac{1}{6} x - 5 = \frac{2}{3} x$

Combine $x$ and $\frac{1}{6}$ .

$- \frac{x}{6} - 5 = \frac{2}{3} x$

Combine $\frac{2}{3}$ and $x$ .

$- \frac{x}{6} - 5 = \frac{2 x}{3}$

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

Subtract $\frac{2 x}{3}$ from both sides of the equation.

$- \frac{x}{6} - 5 - \frac{2 x}{3} = 0$

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

$- \frac{x}{6} - \frac{2 x}{3} \cdot \frac{2}{2} - 5 = 0$

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

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

$- \frac{x}{6} - \frac{2 x \cdot 2}{3 \cdot 2} - 5 = 0$

Multiply $3$ by $2$ .

$- \frac{x}{6} - \frac{2 x \cdot 2}{6} - 5 = 0$

Combine the numerators over the common denominator.

$\frac{- x - 2 x \cdot 2}{6} - 5 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x - 2 x \cdot 2$ .

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - 2 x \cdot 2}{6} - 5 = 0$

Factor $x$ out of $- 2 x \cdot 2$ .

$\frac{x \cdot - 1 + x (- 2 \cdot 2)}{6} - 5 = 0$

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

$\frac{x (- 1 - 2 \cdot 2)}{6} - 5 = 0$

Multiply $- 2$ by $2$ .

$\frac{x (- 1 - 4)}{6} - 5 = 0$

Subtract $4$ from $- 1$ .

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

Move $- 5$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Add $5$ to both sides of the equation.

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

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

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{5} (- \frac{5 x}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

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

Move the leading negative in $- \frac{5 x}{6}$ into the numerator.

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

Factor $6$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{6}{5}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 6$

Solve for x -1/6x-5=2/3x

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