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

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

Step 1

Simplify $\frac{1}{4} y - 3 (\frac{1}{2} y + 3)$ .

Simplify each term.

Combine $\frac{1}{4}$ and $y$ .

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

Combine $\frac{1}{2}$ and $y$ .

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

Apply the distributive property.

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

Combine $- 3$ and $\frac{y}{2}$ .

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

Multiply $- 3$ by $3$ .

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

Move the negative in front of the fraction.

$\frac{y}{4} - \frac{3 y}{2} - 9 = - \frac{3}{4} y$

To write $- \frac{3 y}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{4} - \frac{3 y}{2} \cdot \frac{2}{2} - 9 = - \frac{3}{4} y$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 y}{2}$ by $\frac{2}{2}$ .

$\frac{y}{4} - \frac{3 y \cdot 2}{2 \cdot 2} - 9 = - \frac{3}{4} y$

Multiply $2$ by $2$ .

$\frac{y}{4} - \frac{3 y \cdot 2}{4} - 9 = - \frac{3}{4} y$

Combine the numerators over the common denominator.

$\frac{y - 3 y \cdot 2}{4} - 9 = - \frac{3}{4} y$

Simplify each term.

Simplify the numerator.

Factor $y$ out of $y - 3 y \cdot 2$ .

Raise $y$ to the power of $1$ .

$\frac{y^{1} - 3 y \cdot 2}{4} - 9 = - \frac{3}{4} y$

Factor $y$ out of $y^{1}$ .

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

Factor $y$ out of $- 3 y \cdot 2$ .

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

Factor $y$ out of $y \cdot 1 + y (- 3 \cdot 2)$ .

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

Multiply $- 3$ by $2$ .

$\frac{y (1 - 6)}{4} - 9 = - \frac{3}{4} y$

Subtract $6$ from $1$ .

$\frac{y \cdot - 5}{4} - 9 = - \frac{3}{4} y$

Move $- 5$ to the left of $y$ .

$\frac{- 5 \cdot y}{4} - 9 = - \frac{3}{4} y$

Move the negative in front of the fraction.

$- \frac{5 y}{4} - 9 = - \frac{3}{4} y$

Step 2

Simplify $- \frac{3}{4} y$ .

Combine $y$ and $\frac{3}{4}$ .

$- \frac{5 y}{4} - 9 = - \frac{y \cdot 3}{4}$

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

$- \frac{5 y}{4} - 9 = - \frac{3 y}{4}$

Step 3

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

Add $\frac{3 y}{4}$ to both sides of the equation.

$- \frac{5 y}{4} - 9 + \frac{3 y}{4} = 0$

Combine the numerators over the common denominator.

$- 9 + \frac{- 5 y + 3 y}{4} = 0$

Add $- 5 y$ and $3 y$ .

$- 9 + \frac{- 2 y}{4} = 0$

Simplify each term.

Cancel the common factor of $- 2$ and $4$ .

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

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

Cancel the common factors.

Factor $2$ out of $4$ .

$- 9 + \frac{2 (- y)}{2 (2)} = 0$

Cancel the common factor.

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

Rewrite the expression.

$- 9 + \frac{- y}{2} = 0$

Move the negative in front of the fraction.

$- 9 - \frac{y}{2} = 0$

Step 4

Add $9$ to both sides of the equation.

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

Step 5

Multiply both sides of the equation by $- 2$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{y}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

$2 \cdot - 1 \frac{- y}{2} = - 2 \cdot 9$

Rewrite the expression.

$- - y = - 2 \cdot 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - 2 \cdot 9$

Multiply $y$ by $1$ .

$y = - 2 \cdot 9$

Simplify the right side.

Multiply $- 2$ by $9$ .

$y = - 18$

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

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