Pre-Algebra Examples

$6 - \frac{1}{4} x = \frac{1}{8}$

Step 1

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

$6 - \frac{x}{4} = \frac{1}{8}$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the equation.

$- \frac{x}{4} = \frac{1}{8} - 6$

Step 2.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{x}{4} = \frac{1}{8} - 6 \cdot \frac{8}{8}$

Step 2.3

Combine $- 6$ and $\frac{8}{8}$ .

$- \frac{x}{4} = \frac{1}{8} + \frac{- 6 \cdot 8}{8}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{1 - 6 \cdot 8}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 6$ by $8$ .

$- \frac{x}{4} = \frac{1 - 48}{8}$

Step 2.5.2

Subtract $48$ from $1$ .

$- \frac{x}{4} = \frac{- 47}{8}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{47}{8}$

Step 3

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 (- \frac{47}{8})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

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

$- 4 \frac{- x}{4} = - 4 (- \frac{47}{8})$

Step 4.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (- \frac{47}{8})$

Step 4.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (- \frac{47}{8})$

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 4 (- \frac{47}{8})$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (- \frac{47}{8})$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 4 (- \frac{47}{8})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 4 (- \frac{47}{8})$ .

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Step 4.2.1.1

Cancel the common factor of $4$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{47}{8}$ into the numerator.

$x = - 4 (\frac{- 47}{8})$

Step 4.2.1.1.2

Factor $4$ out of $- 4$ .

$x = 4 (- 1) \frac{- 47}{8}$

Step 4.2.1.1.3

Factor $4$ out of $8$ .

$x = 4 \cdot - 1 \frac{- 47}{4 \cdot 2}$

Step 4.2.1.1.4

Cancel the common factor.

$x = 4 \cdot - 1 \frac{- 47}{4 \cdot 2}$

Step 4.2.1.1.5

Rewrite the expression.

$x = - \frac{- 47}{2}$

Step 4.2.1.2

Move the negative in front of the fraction.

$x = - - \frac{47}{2}$

Step 4.2.1.3

Multiply $- - \frac{47}{2}$ .

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Step 4.2.1.3.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{47}{2})$

Step 4.2.1.3.2

Multiply $\frac{47}{2}$ by $1$ .

$x = \frac{47}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{47}{2}$

Decimal Form:

$x = 23.5$

Mixed Number Form:

$x = 23 \frac{1}{2}$