Solve for y 1/2(2y-4)=2/3(9y+3)

$\frac{1}{2} (2 y - 4) = \frac{2}{3} (9 y + 3)$

Step 1

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

Start simplifying.

$0 + 0 + \frac{1}{2} \cdot (2 y - 4) = \frac{2}{3} \cdot (9 y + 3)$

Simplify by adding zeros.

$\frac{1}{2} \cdot (2 y - 4) = \frac{2}{3} \cdot (9 y + 3)$

Apply the distributive property.

$\frac{1}{2} (2 y) + \frac{1}{2} \cdot - 4 = \frac{2}{3} \cdot (9 y + 3)$

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) + \frac{1}{2} \cdot - 4 = \frac{2}{3} \cdot (9 y + 3)$

Cancel the common factor.

$\frac{1}{2} (2 y) + \frac{1}{2} \cdot - 4 = \frac{2}{3} \cdot (9 y + 3)$

Rewrite the expression.

$y + \frac{1}{2} \cdot - 4 = \frac{2}{3} \cdot (9 y + 3)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$y + \frac{1}{2} \cdot (2 (- 2)) = \frac{2}{3} \cdot (9 y + 3)$

Cancel the common factor.

$y + \frac{1}{2} \cdot (2 \cdot - 2) = \frac{2}{3} \cdot (9 y + 3)$

Rewrite the expression.

$y - 2 = \frac{2}{3} \cdot (9 y + 3)$

Step 2

Simplify $\frac{2}{3} \cdot (9 y + 3)$ .

Apply the distributive property.

$y - 2 = \frac{2}{3} (9 y) + \frac{2}{3} \cdot 3$

Cancel the common factor of $3$ .

Factor $3$ out of $9 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $2$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$y - 2 = 6 y + 2$

Step 3

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

Subtract $6 y$ from both sides of the equation.

$y - 2 - 6 y = 2$

Subtract $6 y$ from $y$ .

$- 5 y - 2 = 2$

Step 4

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

Add $2$ to both sides of the equation.

$- 5 y = 2 + 2$

Add $2$ and $2$ .

$- 5 y = 4$

Step 5

Divide each term in $- 5 y = 4$ by $- 5$ and simplify.

Divide each term in $- 5 y = 4$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{4}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{4}{- 5}$

Divide $y$ by $1$ .

$y = \frac{4}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{4}{5}$

Decimal Form:

$y = - 0.8$

Solve for y 1/2(2y-4)=2/3(9y+3)

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