Solve for x 1/6=1/2-1/4x

$\frac{1}{6} = \frac{1}{2} - \frac{1}{4} x$

Rewrite the equation as $\frac{1}{2} - \frac{1}{4} x = \frac{1}{6}$ .

$\frac{1}{2} - \frac{1}{4} x = \frac{1}{6}$

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

$\frac{1}{2} - \frac{x}{4} = \frac{1}{6}$

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

Subtract $\frac{1}{2}$ from both sides of the equation.

$- \frac{x}{4} = \frac{1}{6} - \frac{1}{2}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{x}{4} = \frac{1}{6} - \frac{1}{2} \cdot \frac{3}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$- \frac{x}{4} = \frac{1}{6} - \frac{3}{2 \cdot 3}$

Multiply $2$ by $3$ .

$- \frac{x}{4} = \frac{1}{6} - \frac{3}{6}$

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{1 - 3}{6}$

Subtract $3$ from $1$ .

$- \frac{x}{4} = \frac{- 2}{6}$

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$- \frac{x}{4} = \frac{2 (- 1)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$- \frac{x}{4} = \frac{2 \cdot - 1}{2 \cdot 3}$

Cancel the common factor.

$- \frac{x}{4} = \frac{2 \cdot - 1}{2 \cdot 3}$

Rewrite the expression.

$- \frac{x}{4} = \frac{- 1}{3}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{1}{3}$

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

$- 4 (- \frac{x}{4}) = - 4 (- \frac{1}{3})$

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.

$- 4 \frac{- x}{4} = - 4 (- \frac{1}{3})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (- \frac{1}{3})$

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (- \frac{1}{3})$

Rewrite the expression.

$- - x = - 4 (- \frac{1}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (- \frac{1}{3})$

Multiply $x$ by $1$ .

$x = - 4 (- \frac{1}{3})$

Simplify the right side.

Multiply $- 4 (- \frac{1}{3})$ .

Multiply $- 1$ by $- 4$ .

$x = 4 (\frac{1}{3})$

Combine $4$ and $\frac{1}{3}$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

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

Solve for x 1/6=1/2-1/4x

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