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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

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

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

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

Factor $x$ out of $- x$ .

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

Factor $x$ out of $x (- 1 \cdot 2) + x \cdot - 1$ .

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

Multiply $- 1$ by $2$ .

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

Subtract $1$ from $- 2$ .

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

Cancel the common factor of $- 3$ and $6$ .

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

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

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move the negative in front of the fraction.

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

Step 4

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $1$ .

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

Step 5

Multiply both sides of the equation by $- 2$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - x = - 2 \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 1$

Multiply $x$ by $1$ .

$x = - 2 \cdot - 1$

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$x = 2$

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

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