Solve for y x-(y+2)=2(2x+1)

$x - (y + 2) = 2 (2 x + 1)$

Step 1

Simplify each term.

Apply the distributive property.

$x - y - 1 \cdot 2 = 2 (2 x + 1)$

Multiply $- 1$ by $2$ .

$x - y - 2 = 2 (2 x + 1)$

Step 2

Simplify $2 (2 x + 1)$ .

Apply the distributive property.

$x - y - 2 = 2 (2 x) + 2 \cdot 1$

Multiply.

Multiply $2$ by $2$ .

$x - y - 2 = 4 x + 2 \cdot 1$

Multiply $2$ by $1$ .

$x - y - 2 = 4 x + 2$

Step 3

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

Subtract $x$ from both sides of the equation.

$- y - 2 = 4 x + 2 - x$

Add $2$ to both sides of the equation.

$- y = 4 x + 2 - x + 2$

Subtract $x$ from $4 x$ .

$- y = 3 x + 2 + 2$

Add $2$ and $2$ .

$- y = 3 x + 4$

Step 4

Divide each term in $- y = 3 x + 4$ by $- 1$ and simplify.

Divide each term in $- y = 3 x + 4$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

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

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

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

Multiply $3$ by $- 1$ .

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

Divide $4$ by $- 1$ .

$y = - 3 x - 4$