Algebra Examples

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

Step 1

Rewrite the equation as $\frac{4}{5} - (x - \frac{4}{5}) + \frac{5}{4} x = 1$ .

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

Step 2

Simplify $\frac{4}{5} - (x - \frac{4}{5}) + \frac{5}{4} x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{4}{5} - x - - \frac{4}{5} + \frac{5}{4} x = 1$

Step 2.1.2

Multiply $- - \frac{4}{5}$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.2.2

Multiply $\frac{4}{5}$ by $1$ .

$\frac{4}{5} - x + \frac{4}{5} + \frac{5}{4} x = 1$

Step 2.1.3

Combine $\frac{5}{4}$ and $x$ .

$\frac{4}{5} - x + \frac{4}{5} + \frac{5 x}{4} = 1$

Step 2.2

Combine fractions.

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Step 2.2.1

Combine the numerators over the common denominator.

$- x + \frac{4 + 4}{5} + \frac{5 x}{4} = 1$

Step 2.2.2

Add $4$ and $4$ .

$- x + \frac{8}{5} + \frac{5 x}{4} = 1$

Step 2.3

To write $- x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- x \cdot \frac{4}{4} + \frac{5 x}{4} + \frac{8}{5} = 1$

Step 2.4

Simplify terms.

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Step 2.4.1

Combine $- x$ and $\frac{4}{4}$ .

$\frac{- x \cdot 4}{4} + \frac{5 x}{4} + \frac{8}{5} = 1$

Step 2.4.2

Combine the numerators over the common denominator.

$\frac{- x \cdot 4 + 5 x}{4} + \frac{8}{5} = 1$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $- x \cdot 4 + 5 x$ .

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Step 2.5.1.1.1

Factor $x$ out of $- x \cdot 4$ .

$\frac{x (- 1 \cdot 4) + 5 x}{4} + \frac{8}{5} = 1$

Step 2.5.1.1.2

Factor $x$ out of $5 x$ .

$\frac{x (- 1 \cdot 4) + x \cdot 5}{4} + \frac{8}{5} = 1$

Step 2.5.1.1.3

Factor $x$ out of $x (- 1 \cdot 4) + x \cdot 5$ .

$\frac{x (- 1 \cdot 4 + 5)}{4} + \frac{8}{5} = 1$

Step 2.5.1.2

Multiply $- 1$ by $4$ .

$\frac{x (- 4 + 5)}{4} + \frac{8}{5} = 1$

Step 2.5.1.3

Add $- 4$ and $5$ .

$\frac{x \cdot 1}{4} + \frac{8}{5} = 1$

Step 2.5.2

Multiply $x$ by $1$ .

$\frac{x}{4} + \frac{8}{5} = 1$

Step 3

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

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Step 3.1

Subtract $\frac{8}{5}$ from both sides of the equation.

$\frac{x}{4} = 1 - \frac{8}{5}$

Step 3.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{4} = \frac{5}{5} - \frac{8}{5}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{x}{4} = \frac{5 - 8}{5}$

Step 3.4

Subtract $8$ from $5$ .

$\frac{x}{4} = \frac{- 3}{5}$

Step 3.5

Move the negative in front of the fraction.

$\frac{x}{4} = - \frac{3}{5}$

Step 4

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (- \frac{3}{5})$

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

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$4 \frac{x}{4} = 4 (- \frac{3}{5})$

Step 5.1.1.2

Rewrite the expression.

$x = 4 (- \frac{3}{5})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $4 (- \frac{3}{5})$ .

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Step 5.2.1.1

Multiply $4 (- \frac{3}{5})$ .

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Step 5.2.1.1.1

Multiply $- 1$ by $4$ .

$x = - 4 (\frac{3}{5})$

Step 5.2.1.1.2

Combine $- 4$ and $\frac{3}{5}$ .

$x = \frac{- 4 \cdot 3}{5}$

Step 5.2.1.1.3

Multiply $- 4$ by $3$ .

$x = \frac{- 12}{5}$

Step 5.2.1.2

Move the negative in front of the fraction.

$x = - \frac{12}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{5}$

Decimal Form:

$x = - 2.4$

Mixed Number Form:

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