Solve for y 11-1/2y=3+6x for y

$11 - \frac{1}{2} y = 3 + 6 x$ for $y$

Step 1

Combine $y$ and $\frac{1}{2}$ .

$11 - \frac{y}{2} = 3 + 6 x$

Step 2

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

Subtract $11$ from both sides of the equation.

$- \frac{y}{2} = 3 + 6 x - 11$

Subtract $11$ from $3$ .

$- \frac{y}{2} = 6 x - 8$

Step 3

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

$- 2 (- \frac{y}{2}) = - 2 (6 x - 8)$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

$- 2 \frac{- y}{2} = - 2 (6 x - 8)$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- y}{2} = - 2 (6 x - 8)$

Cancel the common factor.

$2 \cdot - 1 \frac{- y}{2} = - 2 (6 x - 8)$

Rewrite the expression.

$- - y = - 2 (6 x - 8)$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 2 (6 x - 8)$

Multiply $y$ by $1$ .

$y = - 2 (6 x - 8)$

Simplify the right side.

Simplify $- 2 (6 x - 8)$ .

Apply the distributive property.

$y = - 2 (6 x) - 2 \cdot - 8$

Multiply.

Multiply $6$ by $- 2$ .

$y = - 12 x - 2 \cdot - 8$

Multiply $- 2$ by $- 8$ .

$y = - 12 x + 16$