Solve for y 9/2+5/2y=2y-4

$\frac{9}{2} + \frac{5}{2} y = 2 y - 4$

Step 1

Combine $\frac{5}{2}$ and $y$ .

$\frac{9}{2} + \frac{5 y}{2} = 2 y - 4$

Step 2

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

Subtract $2 y$ from both sides of the equation.

$\frac{9}{2} + \frac{5 y}{2} - 2 y = - 4$

To write $- 2 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9}{2} + \frac{5 y}{2} - 2 y \cdot \frac{2}{2} = - 4$

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

$\frac{9}{2} + \frac{5 y}{2} + \frac{- 2 y \cdot 2}{2} = - 4$

Combine the numerators over the common denominator.

$\frac{9}{2} + \frac{5 y - 2 y \cdot 2}{2} = - 4$

Combine the numerators over the common denominator.

$\frac{9 + 5 y - 2 y \cdot 2}{2} = - 4$

Multiply $2$ by $- 2$ .

$\frac{9 + 5 y - 4 y}{2} = - 4$

Subtract $4 y$ from $5 y$ .

$\frac{9 + y}{2} = - 4$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{9 + y}{2} = 2 \cdot - 4$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{9 + y}{2} = 2 \cdot - 4$

Rewrite the expression.

$9 + y = 2 \cdot - 4$

Simplify the right side.

Multiply $2$ by $- 4$ .

$9 + y = - 8$

Step 5

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

Subtract $9$ from both sides of the equation.

$y = - 8 - 9$

Subtract $9$ from $- 8$ .

$y = - 17$