Algebra Examples

$\frac{1}{6} (x + \frac{1}{5}) = - \frac{17}{15}$

Step 1

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot (x + \frac{1}{5})) = 6 (- \frac{17}{15})$

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 $6 (\frac{1}{6} \cdot (x + \frac{1}{5}))$ .

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Step 2.1.1.1

Apply the distributive property.

$6 (\frac{1}{6} x + \frac{1}{6} \cdot \frac{1}{5}) = 6 (- \frac{17}{15})$

Step 2.1.1.2

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

$6 (\frac{x}{6} + \frac{1}{6} \cdot \frac{1}{5}) = 6 (- \frac{17}{15})$

Step 2.1.1.3

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

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Step 2.1.1.3.1

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

$6 (\frac{x}{6} + \frac{1}{6 \cdot 5}) = 6 (- \frac{17}{15})$

Step 2.1.1.3.2

Multiply $6$ by $5$ .

$6 (\frac{x}{6} + \frac{1}{30}) = 6 (- \frac{17}{15})$

Step 2.1.1.4

Apply the distributive property.

$6 \frac{x}{6} + 6 (\frac{1}{30}) = 6 (- \frac{17}{15})$

Step 2.1.1.5

Cancel the common factor of $6$ .

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Step 2.1.1.5.1

Cancel the common factor.

$6 \frac{x}{6} + 6 (\frac{1}{30}) = 6 (- \frac{17}{15})$

Step 2.1.1.5.2

Rewrite the expression.

$x + 6 (\frac{1}{30}) = 6 (- \frac{17}{15})$

Step 2.1.1.6

Cancel the common factor of $6$ .

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Step 2.1.1.6.1

Factor $6$ out of $30$ .

$x + 6 \frac{1}{6 (5)} = 6 (- \frac{17}{15})$

Step 2.1.1.6.2

Cancel the common factor.

$x + 6 \frac{1}{6 \cdot 5} = 6 (- \frac{17}{15})$

Step 2.1.1.6.3

Rewrite the expression.

$x + \frac{1}{5} = 6 (- \frac{17}{15})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $6 (- \frac{17}{15})$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{17}{15}$ into the numerator.

$x + \frac{1}{5} = 6 (\frac{- 17}{15})$

Step 2.2.1.1.2

Factor $3$ out of $6$ .

$x + \frac{1}{5} = 3 (2) \frac{- 17}{15}$

Step 2.2.1.1.3

Factor $3$ out of $15$ .

$x + \frac{1}{5} = 3 \cdot 2 \frac{- 17}{3 \cdot 5}$

Step 2.2.1.1.4

Cancel the common factor.

$x + \frac{1}{5} = 3 \cdot 2 \frac{- 17}{3 \cdot 5}$

Step 2.2.1.1.5

Rewrite the expression.

$x + \frac{1}{5} = 2 (\frac{- 17}{5})$

Step 2.2.1.2

Combine $2$ and $\frac{- 17}{5}$ .

$x + \frac{1}{5} = \frac{2 \cdot - 17}{5}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $2$ by $- 17$ .

$x + \frac{1}{5} = \frac{- 34}{5}$

Step 2.2.1.3.2

Move the negative in front of the fraction.

$x + \frac{1}{5} = - \frac{34}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{1}{5}$ from both sides of the equation.

$x = - \frac{34}{5} - \frac{1}{5}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 34 - 1}{5}$

Step 3.3

Subtract $1$ from $- 34$ .

$x = \frac{- 35}{5}$

Step 3.4

Divide $- 35$ by $5$ .

$x = - 7$