Algebra Examples

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

Step 1

Rewrite the equation as $- \frac{2}{3} - \frac{1}{6} x = - \frac{1}{5}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Add $\frac{2}{3}$ to both sides of the equation.

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

Step 3.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{5}$ by $\frac{3}{3}$ .

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

Step 3.4.2

Multiply $5$ by $3$ .

$- \frac{x}{6} = - \frac{3}{15} + \frac{2}{3} \cdot \frac{5}{5}$

Step 3.4.3

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$- \frac{x}{6} = - \frac{3}{15} + \frac{2 \cdot 5}{3 \cdot 5}$

Step 3.4.4

Multiply $3$ by $5$ .

$- \frac{x}{6} = - \frac{3}{15} + \frac{2 \cdot 5}{15}$

Step 3.5

Combine the numerators over the common denominator.

$- \frac{x}{6} = \frac{- 3 + 2 \cdot 5}{15}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $2$ by $5$ .

$- \frac{x}{6} = \frac{- 3 + 10}{15}$

Step 3.6.2

Add $- 3$ and $10$ .

$- \frac{x}{6} = \frac{7}{15}$

Step 4

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{x}{6}) = - 6 (\frac{7}{15})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $6$ .

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Step 5.1.1.1.1

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

$- 6 \frac{- x}{6} = - 6 (\frac{7}{15})$

Step 5.1.1.1.2

Factor $6$ out of $- 6$ .

$6 (- 1) \frac{- x}{6} = - 6 (\frac{7}{15})$

Step 5.1.1.1.3

Cancel the common factor.

$6 \cdot - 1 \frac{- x}{6} = - 6 (\frac{7}{15})$

Step 5.1.1.1.4

Rewrite the expression.

$- - x = - 6 (\frac{7}{15})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 6 (\frac{7}{15})$

Step 5.1.1.2.2

Multiply $x$ by $1$ .

$x = - 6 (\frac{7}{15})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 6 (\frac{7}{15})$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $- 6$ .

$x = 3 (- 2) \frac{7}{15}$

Step 5.2.1.1.2

Factor $3$ out of $15$ .

$x = 3 \cdot - 2 \frac{7}{3 \cdot 5}$

Step 5.2.1.1.3

Cancel the common factor.

$x = 3 \cdot - 2 \frac{7}{3 \cdot 5}$

Step 5.2.1.1.4

Rewrite the expression.

$x = - 2 (\frac{7}{5})$

Step 5.2.1.2

Combine $- 2$ and $\frac{7}{5}$ .

$x = \frac{- 2 \cdot 7}{5}$

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $- 2$ by $7$ .

$x = \frac{- 14}{5}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{14}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{14}{5}$

Decimal Form:

$x = - 2.8$

Mixed Number Form:

$x = - 2 \frac{4}{5}$