Simplify 2(x+2)-x+3(-x-2)-(2x+4)

$2 (x + 2) - x + 3 (- x - 2) - (2 x + 4)$

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot 2 - x + 3 (- x - 2) - (2 x + 4)$

Multiply $2$ by $2$ .

$2 x + 4 - x + 3 (- x - 2) - (2 x + 4)$

Apply the distributive property.

$2 x + 4 - x + 3 (- x) + 3 \cdot - 2 - (2 x + 4)$

Multiply $- 1$ by $3$ .

$2 x + 4 - x - 3 x + 3 \cdot - 2 - (2 x + 4)$

Multiply $3$ by $- 2$ .

$2 x + 4 - x - 3 x - 6 - (2 x + 4)$

Apply the distributive property.

$2 x + 4 - x - 3 x - 6 - (2 x) - 1 \cdot 4$

Multiply $2$ by $- 1$ .

$2 x + 4 - x - 3 x - 6 - 2 x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$2 x + 4 - x - 3 x - 6 - 2 x - 4$

Simplify by adding terms.

Combine the opposite terms in $2 x + 4 - x - 3 x - 6 - 2 x - 4$ .

Subtract $2 x$ from $2 x$ .

$4 - x - 3 x - 6 + 0 - 4$

Add $4 - x - 3 x - 6$ and $0$ .

$4 - x - 3 x - 6 - 4$

Subtract $4$ from $4$ .

$- x - 3 x - 6 + 0$

Add $- x - 3 x - 6$ and $0$ .

$- x - 3 x - 6$

Subtract $3 x$ from $- x$ .

$- 4 x - 6$