Solve for x x-2=(4(x+1))/2

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

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

Factor $2$ out of $4 (x + 1)$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 (x + 1)$ by $1$ .

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

Solve for $x$ .

Simplify $2 (x + 1)$ .

Rewrite.

$x - 2 = 0 + 0 + 2 (x + 1)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $2$ by $1$ .

$x - 2 = 2 x + 2$

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

Subtract $2 x$ from both sides of the equation.

$x - 2 - 2 x = 2$

Subtract $2 x$ from $x$ .

$- x - 2 = 2$

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

Add $2$ to both sides of the equation.

$- x = 2 + 2$

Add $2$ and $2$ .

$- x = 4$

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

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

$\frac{- x}{- 1} = \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$x = - 4$