Solve for x x/6-(x-2)/2=(x-13)/9

$\frac{x}{6} - \frac{x - 2}{2} = \frac{x - 13}{9}$

Multiply both sides by $9$ .

$(\frac{x}{6} - \frac{x - 2}{2}) \cdot 9 = \frac{x - 13}{9} \cdot 9$

Simplify.

Simplify the left side.

Simplify $(\frac{x}{6} - \frac{x - 2}{2}) \cdot 9$ .

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

$(\frac{x}{6} - \frac{x - 2}{2} \cdot \frac{3}{3}) \cdot 9 = \frac{x - 13}{9} \cdot 9$

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

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

$(\frac{x}{6} - \frac{(x - 2) \cdot 3}{2 \cdot 3}) \cdot 9 = \frac{x - 13}{9} \cdot 9$

Multiply $2$ by $3$ .

$(\frac{x}{6} - \frac{(x - 2) \cdot 3}{6}) \cdot 9 = \frac{x - 13}{9} \cdot 9$

Combine the numerators over the common denominator.

$\frac{x - (x - 2) \cdot 3}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Simplify the numerator.

Apply the distributive property.

$\frac{x + (- x - - 2) \cdot 3}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Multiply $- 1$ by $- 2$ .

$\frac{x + (- x + 2) \cdot 3}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Apply the distributive property.

$\frac{x - x \cdot 3 + 2 \cdot 3}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Multiply $3$ by $- 1$ .

$\frac{x - 3 x + 2 \cdot 3}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Multiply $2$ by $3$ .

$\frac{x - 3 x + 6}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Subtract $3 x$ from $x$ .

$\frac{- 2 x + 6}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Factor $2$ out of $- 2 x + 6$ .

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

$\frac{2 (- x) + 6}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Factor $2$ out of $6$ .

$\frac{2 (- x) + 2 (3)}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Factor $2$ out of $2 (- x) + 2 (3)$ .

$\frac{2 (- x + 3)}{6} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Simplify terms.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{2 (- x + 3)}{3 (2)} \cdot 9 = \frac{x - 13}{9} \cdot 9$

Factor $3$ out of $9$ .

$\frac{2 (- x + 3)}{3 \cdot 2} \cdot (3 \cdot 3) = \frac{x - 13}{9} \cdot 9$

Cancel the common factor.

$\frac{2 (- x + 3)}{3 \cdot 2} \cdot (3 \cdot 3) = \frac{x - 13}{9} \cdot 9$

Rewrite the expression.

$\frac{2 (- x + 3)}{2} \cdot 3 = \frac{x - 13}{9} \cdot 9$

Combine $\frac{2 (- x + 3)}{2}$ and $3$ .

$\frac{2 (- x + 3) \cdot 3}{2} = \frac{x - 13}{9} \cdot 9$

Multiply $3$ by $2$ .

$\frac{6 (- x + 3)}{2} = \frac{x - 13}{9} \cdot 9$

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

Factor $2$ out of $6 (- x + 3)$ .

$\frac{2 (3 (- x + 3))}{2} = \frac{x - 13}{9} \cdot 9$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (3 (- x + 3))}{2 (1)} = \frac{x - 13}{9} \cdot 9$

Cancel the common factor.

$\frac{2 (3 (- x + 3))}{2 \cdot 1} = \frac{x - 13}{9} \cdot 9$

Rewrite the expression.

$\frac{3 (- x + 3)}{1} = \frac{x - 13}{9} \cdot 9$

Divide $3 (- x + 3)$ by $1$ .

$3 (- x + 3) = \frac{x - 13}{9} \cdot 9$

Apply the distributive property.

$3 (- x) + 3 \cdot 3 = \frac{x - 13}{9} \cdot 9$

Multiply.

Multiply $- 1$ by $3$ .

$- 3 x + 3 \cdot 3 = \frac{x - 13}{9} \cdot 9$

Multiply $3$ by $3$ .

$- 3 x + 9 = \frac{x - 13}{9} \cdot 9$

Simplify the right side.

Cancel the common factor of $9$ .

Cancel the common factor.

$- 3 x + 9 = \frac{x - 13}{9} \cdot 9$

Rewrite the expression.

$- 3 x + 9 = x - 13$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$- 3 x + 9 - x = - 13$

Subtract $x$ from $- 3 x$ .

$- 4 x + 9 = - 13$

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

Subtract $9$ from both sides of the equation.

$- 4 x = - 13 - 9$

Subtract $9$ from $- 13$ .

$- 4 x = - 22$

Divide each term in $- 4 x = - 22$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 22$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 22}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 22}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 22}{- 4}$

Simplify the right side.

Cancel the common factor of $- 22$ and $- 4$ .

Factor $- 2$ out of $- 22$ .

$x = \frac{- 2 (11)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 11}{- 2 \cdot 2}$

Cancel the common factor.

$x = \frac{- 2 \cdot 11}{- 2 \cdot 2}$

Rewrite the expression.

$x = \frac{11}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{2}$

Decimal Form:

$x = 5.5$

Mixed Number Form:

$x = 5 \frac{1}{2}$

Solve for x x/6-(x-2)/2=(x-13)/9

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