Algebra Examples

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

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.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.1.1.2

Cancel the common factor of $6$ .

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.2.3

Cancel the common factor.

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

Step 2.1.1.2.4

Rewrite the expression.

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

Step 2.1.1.3

Multiply.

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Step 2.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.3.2

Multiply $x$ by $1$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

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

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

Step 2.2.1.2

Cancel the common factor.

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

Step 2.2.1.3

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:

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