Solve for x 5/6x+2-x=1/6x

$\frac{5}{6} x + 2 - x = \frac{1}{6} x$

Step 1

Simplify $\frac{5}{6} x + 2 - x$ .

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} + 2 - x = \frac{1}{6} x$

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

$\frac{5 x}{6} - x \cdot \frac{6}{6} + 2 = \frac{1}{6} x$

Simplify terms.

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

$\frac{5 x}{6} + \frac{- x \cdot 6}{6} + 2 = \frac{1}{6} x$

Combine the numerators over the common denominator.

$\frac{5 x - x \cdot 6}{6} + 2 = \frac{1}{6} x$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - x \cdot 6$ .

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - x \cdot 6}{6} + 2 = \frac{1}{6} x$

Factor $x$ out of $- x \cdot 6$ .

$\frac{x \cdot 5 + x (- 1 \cdot 6)}{6} + 2 = \frac{1}{6} x$

Factor $x$ out of $x \cdot 5 + x (- 1 \cdot 6)$ .

$\frac{x (5 - 1 \cdot 6)}{6} + 2 = \frac{1}{6} x$

Multiply $- 1$ by $6$ .

$\frac{x (5 - 6)}{6} + 2 = \frac{1}{6} x$

Subtract $6$ from $5$ .

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

Move $- 1$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Step 2

Combine $\frac{1}{6}$ and $x$ .

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

Step 3

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

Subtract $\frac{x}{6}$ from both sides of the equation.

$- \frac{x}{6} + 2 - \frac{x}{6} = 0$

Combine the numerators over the common denominator.

$2 + \frac{- x - x}{6} = 0$

Subtract $x$ from $- x$ .

$2 + \frac{- 2 x}{6} = 0$

Simplify each term.

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

Factor $2$ out of $- 2 x$ .

$2 + \frac{2 (- x)}{6} = 0$

Cancel the common factors.

Factor $2$ out of $6$ .

$2 + \frac{2 (- x)}{2 (3)} = 0$

Cancel the common factor.

$2 + \frac{2 (- x)}{2 \cdot 3} = 0$

Rewrite the expression.

$2 + \frac{- x}{3} = 0$

Move the negative in front of the fraction.

$2 - \frac{x}{3} = 0$

Step 4

Subtract $2$ from both sides of the equation.

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

Step 5

Multiply both sides of the equation by $- 3$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 3 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 3 \cdot - 2$

Multiply $x$ by $1$ .

$x = - 3 \cdot - 2$

Simplify the right side.

Multiply $- 3$ by $- 2$ .

$x = 6$

Solve for x 5/6x+2-x=1/6x

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