Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

$x - 2 = 0 + 0 - \frac{1}{4} \cdot (x - 8)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Combine $x$ and $\frac{1}{4}$ .

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

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 1.5.2

Factor $4$ out of $- 8$ .

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

Step 1.5.3

Cancel the common factor.

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

Step 1.5.4

Rewrite the expression.

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

Step 1.6

Multiply $- 1$ by $- 2$ .

$x - 2 = - \frac{x}{4} + 2$

Step 2

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

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Step 2.1

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

$x - 2 + \frac{x}{4} = 2$

Step 2.2

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

$x \cdot \frac{4}{4} + \frac{x}{4} - 2 = 2$

Step 2.3

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

$\frac{x \cdot 4}{4} + \frac{x}{4} - 2 = 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 + x}{4} - 2 = 2$

Step 2.5

Add $x \cdot 4$ and $x$ .

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Step 2.5.1

Reorder $x$ and $4$ .

$\frac{4 \cdot x + x}{4} - 2 = 2$

Step 2.5.2

Add $4 \cdot x$ and $x$ .

$\frac{5 \cdot x}{4} - 2 = 2$

$\frac{5 x}{4} - 2 = 2$

Step 3

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

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Step 3.1

Add $2$ to both sides of the equation.

$\frac{5 x}{4} = 2 + 2$

Step 3.2

Add $2$ and $2$ .

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

Step 4

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

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

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

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 x$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.2

Simplify the right side.

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Step 5.2.1

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

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Step 5.2.1.1

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

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

Step 5.2.1.2

Multiply $4$ by $4$ .

$x = \frac{16}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{5}$

Decimal Form:

$x = 3.2$

Mixed Number Form:

$x = 3 \frac{1}{5}$