Algebra Examples

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

Step 1

Multiply both sides by $8$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{1}{4} - x) \cdot 8$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Factor $4$ out of $8$ .

$\frac{1}{4} \cdot (4 (2)) - x \cdot 8 = \frac{x}{8} \cdot 8$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 \cdot 2) - x \cdot 8 = \frac{x}{8} \cdot 8$

Step 2.1.1.2.3

Rewrite the expression.

$2 - x \cdot 8 = \frac{x}{8} \cdot 8$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Multiply $8$ by $- 1$ .

$2 - 8 x = \frac{x}{8} \cdot 8$

Step 2.1.1.3.2

Reorder $2$ and $- 8 x$ .

$- 8 x + 2 = \frac{x}{8} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$- 8 x + 2 = \frac{x}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$- 8 x + 2 = x$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$- 8 x + 2 - x = 0$

Step 3.1.2

Subtract $x$ from $- 8 x$ .

$- 9 x + 2 = 0$

Step 3.2

Subtract $2$ from both sides of the equation.

$- 9 x = - 2$

Step 3.3

Divide each term in $- 9 x = - 2$ by $- 9$ and simplify.

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Step 3.3.1

Divide each term in $- 9 x = - 2$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 2}{- 9}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 9$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 2}{- 9}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 9}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$x = \frac{2}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{9}$

Decimal Form:

$x = 0.\overline{2}$