Solve for y 1/2(4-14y)=y+50

$\frac{1}{2} (4 - 14 y) = y + 50$

Simplify $\frac{1}{2} \cdot (4 - 14 y)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (4 - 14 y) = y + 50$

Simplify by adding zeros.

$\frac{1}{2} \cdot (4 - 14 y) = y + 50$

Apply the distributive property.

$\frac{1}{2} \cdot 4 + \frac{1}{2} (- 14 y) = y + 50$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) + \frac{1}{2} (- 14 y) = y + 50$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) + \frac{1}{2} (- 14 y) = y + 50$

Rewrite the expression.

$2 + \frac{1}{2} (- 14 y) = y + 50$

Cancel the common factor of $2$ .

Factor $2$ out of $- 14 y$ .

$2 + \frac{1}{2} (2 (- 7 y)) = y + 50$

Cancel the common factor.

$2 + \frac{1}{2} (2 (- 7 y)) = y + 50$

Rewrite the expression.

$2 - 7 y = y + 50$

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

Subtract $y$ from both sides of the equation.

$2 - 7 y - y = 50$

Subtract $y$ from $- 7 y$ .

$2 - 8 y = 50$

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

Subtract $2$ from both sides of the equation.

$- 8 y = 50 - 2$

Subtract $2$ from $50$ .

$- 8 y = 48$

Divide each term in $- 8 y = 48$ by $- 8$ and simplify.

Divide each term in $- 8 y = 48$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{48}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{48}{- 8}$

Divide $y$ by $1$ .

$y = \frac{48}{- 8}$

Simplify the right side.

Divide $48$ by $- 8$ .

$y = - 6$