Solve for x (x-1)/3-(x-5)/2=1/6

$\frac{x - 1}{3} - \frac{x - 5}{2} = \frac{1}{6}$

Simplify $\frac{x - 1}{3} - \frac{x - 5}{2}$ .

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

$\frac{x - 1}{3} \cdot \frac{2}{2} - \frac{x - 5}{2} = \frac{1}{6}$

To write $- \frac{x - 5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x - 1}{3} \cdot \frac{2}{2} - \frac{x - 5}{2} \cdot \frac{3}{3} = \frac{1}{6}$

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

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

$\frac{(x - 1) \cdot 2}{3 \cdot 2} - \frac{x - 5}{2} \cdot \frac{3}{3} = \frac{1}{6}$

Multiply $3$ by $2$ .

$\frac{(x - 1) \cdot 2}{6} - \frac{x - 5}{2} \cdot \frac{3}{3} = \frac{1}{6}$

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

$\frac{(x - 1) \cdot 2}{6} - \frac{(x - 5) \cdot 3}{2 \cdot 3} = \frac{1}{6}$

Multiply $2$ by $3$ .

$\frac{(x - 1) \cdot 2}{6} - \frac{(x - 5) \cdot 3}{6} = \frac{1}{6}$

Combine the numerators over the common denominator.

$\frac{(x - 1) \cdot 2 - (x - 5) \cdot 3}{6} = \frac{1}{6}$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 2 - 1 \cdot 2 - (x - 5) \cdot 3}{6} = \frac{1}{6}$

Move $2$ to the left of $x$ .

$\frac{2 \cdot x - 1 \cdot 2 - (x - 5) \cdot 3}{6} = \frac{1}{6}$

Multiply $- 1$ by $2$ .

$\frac{2 \cdot x - 2 - (x - 5) \cdot 3}{6} = \frac{1}{6}$

Apply the distributive property.

$\frac{2 x - 2 + (- x - - 5) \cdot 3}{6} = \frac{1}{6}$

Multiply $- 1$ by $- 5$ .

$\frac{2 x - 2 + (- x + 5) \cdot 3}{6} = \frac{1}{6}$

Apply the distributive property.

$\frac{2 x - 2 - x \cdot 3 + 5 \cdot 3}{6} = \frac{1}{6}$

Multiply $3$ by $- 1$ .

$\frac{2 x - 2 - 3 x + 5 \cdot 3}{6} = \frac{1}{6}$

Multiply $5$ by $3$ .

$\frac{2 x - 2 - 3 x + 15}{6} = \frac{1}{6}$

Subtract $3 x$ from $2 x$ .

$\frac{- x - 2 + 15}{6} = \frac{1}{6}$

Add $- 2$ and $15$ .

$\frac{- x + 13}{6} = \frac{1}{6}$

Simplify with factoring out.

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 13}{6} = \frac{1}{6}$

Rewrite $13$ as $- 1 (- 13)$ .

$\frac{- (x) - 1 (- 13)}{6} = \frac{1}{6}$

Factor $- 1$ out of $- (x) - 1 (- 13)$ .

$\frac{- (x - 13)}{6} = \frac{1}{6}$

Simplify the expression.

Rewrite $- (x - 13)$ as $- 1 (x - 13)$ .

$\frac{- 1 (x - 13)}{6} = \frac{1}{6}$

Move the negative in front of the fraction.

$- \frac{x - 13}{6} = \frac{1}{6}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (x - 13) = 1$

Simplify $- (x - 13)$ .

Apply the distributive property.

$- x - - 13 = 1$

Multiply $- 1$ by $- 13$ .

$- x + 13 = 1$

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

Subtract $13$ from both sides of the equation.

$- x = 1 - 13$

Subtract $13$ from $1$ .

$- x = - 12$

Divide each term in $- x = - 12$ by $- 1$ and simplify.

Divide each term in $- x = - 12$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 12}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 1}$

Simplify the right side.

Divide $- 12$ by $- 1$ .

$x = 12$

Solve for x (x-1)/3-(x-5)/2=1/6

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