Solve for x -1/3-1/12x=-1/2

$- \frac{1}{3} - \frac{1}{12} x = - \frac{1}{2}$

Step 1

Combine $x$ and $\frac{1}{12}$ .

$- \frac{1}{3} - \frac{x}{12} = - \frac{1}{2}$

Step 2

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

Add $\frac{1}{3}$ to both sides of the equation.

$- \frac{x}{12} = - \frac{1}{2} + \frac{1}{3}$

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

$- \frac{x}{12} = - \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3}$

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

$- \frac{x}{12} = - \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2}$

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

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

$- \frac{x}{12} = - \frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$- \frac{x}{12} = - \frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2}$

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

$- \frac{x}{12} = - \frac{3}{6} + \frac{2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{x}{12} = - \frac{3}{6} + \frac{2}{6}$

Combine the numerators over the common denominator.

$- \frac{x}{12} = \frac{- 3 + 2}{6}$

Add $- 3$ and $2$ .

$- \frac{x}{12} = \frac{- 1}{6}$

Move the negative in front of the fraction.

$- \frac{x}{12} = - \frac{1}{6}$

Step 3

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{x}{12}) = - 12 (- \frac{1}{6})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 12 (- \frac{x}{12})$ .

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{x}{12}$ into the numerator.

$- 12 \frac{- x}{12} = - 12 (- \frac{1}{6})$

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- x}{12} = - 12 (- \frac{1}{6})$

Cancel the common factor.

$12 \cdot - 1 \frac{- x}{12} = - 12 (- \frac{1}{6})$

Rewrite the expression.

$- - x = - 12 (- \frac{1}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 12 (- \frac{1}{6})$

Multiply $x$ by $1$ .

$x = - 12 (- \frac{1}{6})$

Simplify the right side.

Simplify $- 12 (- \frac{1}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$x = - 12 (\frac{- 1}{6})$

Factor $6$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 2 \cdot - 1$

Multiply $- 2$ by $- 1$ .

$x = 2$

Solve for x -1/3-1/12x=-1/2

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