Solve for y 12-(4y+8)=0.5(8y-16)

$12 - (4 y + 8) = 0.5 (8 y - 16)$

Step 1

Simplify $12 - (4 y + 8)$ .

Simplify each term.

Apply the distributive property.

$12 - (4 y) - 1 \cdot 8 = 0.5 (8 y - 16)$

Multiply $4$ by $- 1$ .

$12 - 4 y - 1 \cdot 8 = 0.5 (8 y - 16)$

Multiply $- 1$ by $8$ .

$12 - 4 y - 8 = 0.5 (8 y - 16)$

Subtract $8$ from $12$ .

$- 4 y + 4 = 0.5 (8 y - 16)$

Step 2

Simplify $0.5 (8 y - 16)$ .

Apply the distributive property.

$- 4 y + 4 = 0.5 (8 y) + 0.5 \cdot - 16$

Multiply.

Multiply $8$ by $0.5$ .

$- 4 y + 4 = 4 y + 0.5 \cdot - 16$

Multiply $0.5$ by $- 16$ .

$- 4 y + 4 = 4 y - 8$

Step 3

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

Subtract $4 y$ from both sides of the equation.

$- 4 y + 4 - 4 y = - 8$

Subtract $4 y$ from $- 4 y$ .

$- 8 y + 4 = - 8$

Step 4

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

Subtract $4$ from both sides of the equation.

$- 8 y = - 8 - 4$

Subtract $4$ from $- 8$ .

$- 8 y = - 12$

Step 5

Divide each term in $- 8 y = - 12$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 12$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 12}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 12}{- 8}$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 8}$

Simplify the right side.

Cancel the common factor of $- 12$ and $- 8$ .

Factor $- 4$ out of $- 12$ .

$y = \frac{- 4 (3)}{- 8}$

Cancel the common factors.

Factor $- 4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{3}{2}$

Decimal Form:

$y = 1.5$

Mixed Number Form:

$y = 1 \frac{1}{2}$

Solve for y 12-(4y+8)=0.5(8y-16)

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