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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $1$ .

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

Multiply $- 1$ by $2$ .

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

Apply the distributive property.

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

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

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

Multiply $- 1$ by $1$ .

$2 - 2 y - \frac{y}{2} - \frac{1}{2} = 3$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

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

Subtract $1$ from $4$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $- 2$ .

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

Subtract $y$ from $- 4 y$ .

$\frac{- 5 y + 3}{2} = 3$

Factor $- 1$ out of $- 5 y$ .

$\frac{- (5 y) + 3}{2} = 3$

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{- (5 y) - 1 (- 3)}{2} = 3$

Factor $- 1$ out of $- (5 y) - 1 (- 3)$ .

$\frac{- (5 y - 3)}{2} = 3$

Simplify the expression.

Rewrite $- (5 y - 3)$ as $- 1 (5 y - 3)$ .

$\frac{- 1 (5 y - 3)}{2} = 3$

Move the negative in front of the fraction.

$- \frac{5 y - 3}{2} = 3$

Step 2

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

$- 2 (- \frac{5 y - 3}{2}) = - 2 \cdot 3$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{5 y - 3}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 y - 3}{2}$ into the numerator.

$- 2 \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Cancel the common factor.

$2 \cdot - 1 \frac{- (5 y - 3)}{2} = - 2 \cdot 3$

Rewrite the expression.

$- - (5 y - 3) = - 2 \cdot 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (5 y - 3) = - 2 \cdot 3$

Multiply $5 y - 3$ by $1$ .

$5 y - 3 = - 2 \cdot 3$

Simplify the right side.

Multiply $- 2$ by $3$ .

$5 y - 3 = - 6$

Step 4

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

Add $3$ to both sides of the equation.

$5 y = - 6 + 3$

Add $- 6$ and $3$ .

$5 y = - 3$

Step 5

Divide each term in $5 y = - 3$ by $5$ and simplify.

Divide each term in $5 y = - 3$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 0.6$

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

Related Questions