Solve for x 1/8=1-1/4x

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

Step 1

Rewrite the equation as $1 - \frac{1}{4} x = \frac{1}{8}$ .

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

Step 2

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

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

Step 3

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

Subtract $1$ from both sides of the equation.

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

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Combine $- 1$ and $\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 1$ by $8$ .

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

Subtract $8$ from $1$ .

$- \frac{x}{4} = \frac{- 7}{8}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{7}{8}$

Step 4

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

$- 4 (- \frac{x}{4}) = - 4 (- \frac{7}{8})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

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

$- 4 \frac{- x}{4} = - 4 (- \frac{7}{8})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (- \frac{7}{8})$

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (- \frac{7}{8})$

Rewrite the expression.

$- - x = - 4 (- \frac{7}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (- \frac{7}{8})$

Multiply $x$ by $1$ .

$x = - 4 (- \frac{7}{8})$

Simplify the right side.

Simplify $- 4 (- \frac{7}{8})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$x = - 4 (\frac{- 7}{8})$

Factor $4$ out of $- 4$ .

$x = 4 (- 1) \frac{- 7}{8}$

Factor $4$ out of $8$ .

$x = 4 \cdot - 1 \frac{- 7}{4 \cdot 2}$

Cancel the common factor.

$x = 4 \cdot - 1 \frac{- 7}{4 \cdot 2}$

Rewrite the expression.

$x = - \frac{- 7}{2}$

Move the negative in front of the fraction.

$x = - - \frac{7}{2}$

Multiply $- - \frac{7}{2}$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{7}{2})$

Multiply $\frac{7}{2}$ by $1$ .

$x = \frac{7}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

$x = 3 \frac{1}{2}$

Solve for x 1/8=1-1/4x

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