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

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

Step 1

Simplify each term.

Combine $y$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $y$ .

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

Step 2

Subtract $x$ from both sides of the equation.

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

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 y}{2}) = - \frac{2}{3} (- 12 - x)$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{3} (- \frac{3 y}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 y}{2}) = - \frac{2}{3} (- 12 - x)$

Move the leading negative in $- \frac{3 y}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 y}{2} = - \frac{2}{3} (- 12 - x)$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 y}{2} = - \frac{2}{3} (- 12 - x)$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 y}{2} = - \frac{2}{3} (- 12 - x)$

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - y = - \frac{2}{3} (- 12 - x)$

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $y$ by $1$ .

$y = - \frac{2}{3} (- 12 - x)$

Simplify the right side.

Simplify $- \frac{2}{3} (- 12 - x)$ .

Apply the distributive property.

$y = - \frac{2}{3} \cdot - 12 - \frac{2}{3} (- x)$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$y = \frac{- 2}{3} \cdot - 12 - \frac{2}{3} (- x)$

Factor $3$ out of $- 12$ .

$y = \frac{- 2}{3} \cdot (3 (- 4)) - \frac{2}{3} (- x)$

Cancel the common factor.

$y = \frac{- 2}{3} \cdot (3 \cdot - 4) - \frac{2}{3} (- x)$

Rewrite the expression.

$y = - 2 \cdot - 4 - \frac{2}{3} (- x)$

Multiply $- 2$ by $- 4$ .

$y = 8 - \frac{2}{3} (- x)$

Multiply $- \frac{2}{3} (- x)$ .

Multiply $- 1$ by $- 1$ .

$y = 8 + 1 (\frac{2}{3}) x$

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

$y = 8 + \frac{2}{3} x$

Combine $\frac{2}{3}$ and $x$ .

$y = 8 + \frac{2 x}{3}$

Step 5

Reorder $8$ and $\frac{2 x}{3}$ .

$y = \frac{2 x}{3} + 8$

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

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