Algebra Examples

$\frac{1}{5} (x - \frac{6}{5}) = - \frac{51}{25}$

Step 1

Multiply both sides of the equation by $5$ .

$5 (\frac{1}{5} \cdot (x - \frac{6}{5})) = 5 (- \frac{51}{25})$

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

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Step 2.1.1.1

Apply the distributive property.

$5 (\frac{1}{5} x + \frac{1}{5} (- \frac{6}{5})) = 5 (- \frac{51}{25})$

Step 2.1.1.2

Combine $\frac{1}{5}$ and $x$ .

$5 (\frac{x}{5} + \frac{1}{5} (- \frac{6}{5})) = 5 (- \frac{51}{25})$

Step 2.1.1.3

Multiply $\frac{1}{5} (- \frac{6}{5})$ .

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Step 2.1.1.3.1

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

$5 (\frac{x}{5} - \frac{6}{5 \cdot 5}) = 5 (- \frac{51}{25})$

Step 2.1.1.3.2

Multiply $5$ by $5$ .

$5 (\frac{x}{5} - \frac{6}{25}) = 5 (- \frac{51}{25})$

Step 2.1.1.4

Apply the distributive property.

$5 \frac{x}{5} + 5 (- \frac{6}{25}) = 5 (- \frac{51}{25})$

Step 2.1.1.5

Cancel the common factor of $5$ .

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Step 2.1.1.5.1

Cancel the common factor.

$5 \frac{x}{5} + 5 (- \frac{6}{25}) = 5 (- \frac{51}{25})$

Step 2.1.1.5.2

Rewrite the expression.

$x + 5 (- \frac{6}{25}) = 5 (- \frac{51}{25})$

Step 2.1.1.6

Cancel the common factor of $5$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{6}{25}$ into the numerator.

$x + 5 (\frac{- 6}{25}) = 5 (- \frac{51}{25})$

Step 2.1.1.6.2

Factor $5$ out of $25$ .

$x + 5 \frac{- 6}{5 (5)} = 5 (- \frac{51}{25})$

Step 2.1.1.6.3

Cancel the common factor.

$x + 5 \frac{- 6}{5 \cdot 5} = 5 (- \frac{51}{25})$

Step 2.1.1.6.4

Rewrite the expression.

$x + \frac{- 6}{5} = 5 (- \frac{51}{25})$

Step 2.1.1.7

Move the negative in front of the fraction.

$x - \frac{6}{5} = 5 (- \frac{51}{25})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $5 (- \frac{51}{25})$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{51}{25}$ into the numerator.

$x - \frac{6}{5} = 5 (\frac{- 51}{25})$

Step 2.2.1.1.2

Factor $5$ out of $25$ .

$x - \frac{6}{5} = 5 \frac{- 51}{5 (5)}$

Step 2.2.1.1.3

Cancel the common factor.

$x - \frac{6}{5} = 5 \frac{- 51}{5 \cdot 5}$

Step 2.2.1.1.4

Rewrite the expression.

$x - \frac{6}{5} = \frac{- 51}{5}$

Step 2.2.1.2

Move the negative in front of the fraction.

$x - \frac{6}{5} = - \frac{51}{5}$

Step 3

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

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Step 3.1

Add $\frac{6}{5}$ to both sides of the equation.

$x = - \frac{51}{5} + \frac{6}{5}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 51 + 6}{5}$

Step 3.3

Add $- 51$ and $6$ .

$x = \frac{- 45}{5}$

Step 3.4

Divide $- 45$ by $5$ .

$x = - 9$