Solve for y -1/2(-5y+4)=2+1/2y

$- \frac{1}{2} (- 5 y + 4) = 2 + \frac{1}{2} y$

Step 1

Simplify $- \frac{1}{2} \cdot (- 5 y + 4)$ .

Rewrite.

$0 + 0 - \frac{1}{2} \cdot (- 5 y + 4) = 2 + \frac{1}{2} y$

Simplify by adding zeros.

$- \frac{1}{2} \cdot (- 5 y + 4) = 2 + \frac{1}{2} y$

Apply the distributive property.

$- \frac{1}{2} (- 5 y) - \frac{1}{2} \cdot 4 = 2 + \frac{1}{2} y$

Multiply $- \frac{1}{2} (- 5 y)$ .

Multiply $- 5$ by $- 1$ .

$5 (\frac{1}{2}) y - \frac{1}{2} \cdot 4 = 2 + \frac{1}{2} y$

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} y - \frac{1}{2} \cdot 4 = 2 + \frac{1}{2} y$

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

$\frac{5 y}{2} - \frac{1}{2} \cdot 4 = 2 + \frac{1}{2} y$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{5 y}{2} + \frac{- 1}{2} \cdot 4 = 2 + \frac{1}{2} y$

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 y}{2} - 1 \cdot 2 = 2 + \frac{1}{2} y$

Multiply $- 1$ by $2$ .

$\frac{5 y}{2} - 2 = 2 + \frac{1}{2} y$

Step 2

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

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

Step 3

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

Subtract $\frac{y}{2}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $y$ from $5 y$ .

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

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

Factor $2$ out of $4 y$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 y$ by $1$ .

$- 2 + 2 y = 2$

Step 4

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

Add $2$ to both sides of the equation.

$2 y = 2 + 2$

Add $2$ and $2$ .

$2 y = 4$

Step 5

Divide each term in $2 y = 4$ by $2$ and simplify.

Divide each term in $2 y = 4$ by $2$ .

$\frac{2 y}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{4}{2}$

Divide $y$ by $1$ .

$y = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$y = 2$

Solve for y -1/2(-5y+4)=2+1/2y

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