Algebra Examples

\frac{1}{4} (x - \frac{4}{5}) = - \frac{39}{20}

$\frac{1}{4} (x - \frac{4}{5}) = - \frac{39}{20}$

Step 1

Multiply both sides of the equation by

$4$ .

$4 (\frac{1}{4} \cdot (x - \frac{4}{5})) = 4 (- \frac{39}{20})$

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

$4 (\frac{1}{4} \cdot (x - \frac{4}{5}))$ .

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Step 2.1.1.1

Apply the distributive property.

$4 (\frac{1}{4} x + \frac{1}{4} (- \frac{4}{5})) = 4 (- \frac{39}{20})$

Step 2.1.1.2

Combine

$\frac{1}{4}$ and

$x$ .

$4 (\frac{x}{4} + \frac{1}{4} (- \frac{4}{5})) = 4 (- \frac{39}{20})$

Step 2.1.1.3

Cancel the common factor of

$4$ .

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Step 2.1.1.3.1

Move the leading negative in

$- \frac{4}{5}$ into the numerator.

$4 (\frac{x}{4} + \frac{1}{4} \cdot \frac{- 4}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.3.2

Factor

$4$ out of

$- 4$ .

$4 (\frac{x}{4} + \frac{1}{4} \cdot \frac{4 (- 1)}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.3.3

Cancel the common factor.

$4 (\frac{x}{4} + \frac{1}{4} \cdot \frac{4 \cdot - 1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.3.4

Rewrite the expression.

$4 (\frac{x}{4} + \frac{- 1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.4

Move the negative in front of the fraction.

$4 (\frac{x}{4} - \frac{1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.5

Apply the distributive property.

$4 \frac{x}{4} + 4 (- \frac{1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.6

Cancel the common factor of

$4$ .

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Step 2.1.1.6.1

Cancel the common factor.

$4 \frac{x}{4} + 4 (- \frac{1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.6.2

Rewrite the expression.

$x + 4 (- \frac{1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.7

Multiply

$4 (- \frac{1}{5})$ .

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Step 2.1.1.7.1

Multiply

$- 1$ by

$4$ .

$x - 4 (\frac{1}{5}) = 4 (- \frac{39}{20})$

Step 2.1.1.7.2

Combine

$- 4$ and

$\frac{1}{5}$ .

$x + \frac{- 4}{5} = 4 (- \frac{39}{20})$

Step 2.1.1.8

Move the negative in front of the fraction.

$x - \frac{4}{5} = 4 (- \frac{39}{20})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify

$4 (- \frac{39}{20})$ .

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Step 2.2.1.1

Cancel the common factor of

$4$ .

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Step 2.2.1.1.1

Move the leading negative in

$- \frac{39}{20}$ into the numerator.

$x - \frac{4}{5} = 4 (\frac{- 39}{20})$

Step 2.2.1.1.2

Factor

$4$ out of

$20$ .

$x - \frac{4}{5} = 4 \frac{- 39}{4 (5)}$

Step 2.2.1.1.3

Cancel the common factor.

$x - \frac{4}{5} = 4 \frac{- 39}{4 \cdot 5}$

Step 2.2.1.1.4

Rewrite the expression.

$x - \frac{4}{5} = \frac{- 39}{5}$

Step 2.2.1.2

Move the negative in front of the fraction.

$x - \frac{4}{5} = - \frac{39}{5}$

Step 3

Move all terms not containing

$x$ to the right side of the equation.

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Step 3.1

Add

$\frac{4}{5}$ to both sides of the equation.

$x = - \frac{39}{5} + \frac{4}{5}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 39 + 4}{5}$

Step 3.3

Add

$- 39$ and

$4$ .

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

Step 3.4

Divide

$- 35$ by

$5$ .

$x = - 7$