Solve for x x/4+2/3=x-1/6

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

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - x \cdot 4$ .

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Factor $x$ out of $- x \cdot 4$ .

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

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 4)$ .

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

Multiply $- 1$ by $4$ .

$\frac{x (1 - 4)}{4} + \frac{2}{3} = - \frac{1}{6}$

Subtract $4$ from $1$ .

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

Move $- 3$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

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

Subtract $\frac{2}{3}$ from both sides of the equation.

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $- 1$ .

$- \frac{3 x}{4} = \frac{- 5}{6}$

Move the negative in front of the fraction.

$- \frac{3 x}{4} = - \frac{5}{6}$

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{5}{6})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) = - \frac{4}{3} (- \frac{5}{6})$

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{5}{6})$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{5}{6})$

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} = - \frac{4}{3} (- \frac{5}{6})$

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{4}{3} (- \frac{5}{6})$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{5}{6})$

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{4}{3} (- \frac{5}{6})$

Rewrite the expression.

$- - x = - \frac{4}{3} (- \frac{5}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{3} (- \frac{5}{6})$

Multiply $x$ by $1$ .

$x = - \frac{4}{3} (- \frac{5}{6})$

Simplify the right side.

Simplify $- \frac{4}{3} (- \frac{5}{6})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x = \frac{- 4}{3} (- \frac{5}{6})$

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$x = \frac{- 4}{3} \cdot \frac{- 5}{6}$

Factor $2$ out of $- 4$ .

$x = \frac{2 (- 2)}{3} \cdot \frac{- 5}{6}$

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 2}{3} \cdot \frac{- 5}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot - 2}{3} \cdot \frac{- 5}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 2}{3} \cdot \frac{- 5}{3}$

Multiply $\frac{- 2}{3}$ by $\frac{- 5}{3}$ .

$x = \frac{- 2 \cdot - 5}{3 \cdot 3}$

Multiply.

Multiply $- 2$ by $- 5$ .

$x = \frac{10}{3 \cdot 3}$

Multiply $3$ by $3$ .

$x = \frac{10}{9}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{9}$

Decimal Form:

$x = 1.\overline{1}$

Mixed Number Form:

$x = 1 \frac{1}{9}$

Solve for x x/4+2/3=x-1/6

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