Solve for y 1/5y+11=3-3/5y

$\frac{1}{5} y + 11 = 3 - \frac{3}{5} y$

Step 1

Combine $\frac{1}{5}$ and $y$ .

$\frac{y}{5} + 11 = 3 - \frac{3}{5} y$

Step 2

Simplify each term.

Combine $y$ and $\frac{3}{5}$ .

$\frac{y}{5} + 11 = 3 - \frac{y \cdot 3}{5}$

Move $3$ to the left of $y$ .

$\frac{y}{5} + 11 = 3 - \frac{3 y}{5}$

Step 3

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

Add $\frac{3 y}{5}$ to both sides of the equation.

$\frac{y}{5} + 11 + \frac{3 y}{5} = 3$

Combine the numerators over the common denominator.

$11 + \frac{y + 3 y}{5} = 3$

Add $y$ and $3 y$ .

$11 + \frac{4 y}{5} = 3$

Step 4

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

Subtract $11$ from both sides of the equation.

$\frac{4 y}{5} = 3 - 11$

Subtract $11$ from $3$ .

$\frac{4 y}{5} = - 8$

Step 5

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 y}{5} = \frac{5}{4} \cdot - 8$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{4} \cdot \frac{4 y}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 y}{5} = \frac{5}{4} \cdot - 8$

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{5}{4} \cdot - 8$

Cancel the common factor of $4$ .

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{5}{4} \cdot - 8$

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{5}{4} \cdot - 8$

Rewrite the expression.

$y = \frac{5}{4} \cdot - 8$

Simplify the right side.

Simplify $\frac{5}{4} \cdot - 8$ .

Cancel the common factor of $4$ .

Factor $4$ out of $- 8$ .

$y = \frac{5}{4} \cdot (4 (- 2))$

Cancel the common factor.

$y = \frac{5}{4} \cdot (4 \cdot - 2)$

Rewrite the expression.

$y = 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$y = - 10$

Solve for y 1/5y+11=3-3/5y

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