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

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

Step 1

Multiply both sides of the equation by $- \frac{1}{6}$ .

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

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{1}{6} \cdot \frac{x}{- \frac{1}{6}}$ .

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

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

Factor $6$ out of $x (- 1 \cdot 6)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.\overline{142857}$