Solve for x -3(x+2)-1=1+2(1-2x)

$- 3 (x + 2) - 1 = 1 + 2 (1 - 2 x)$

Simplify $- 3 (x + 2) - 1$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 3 \cdot 2 - 1 = 1 + 2 (1 - 2 x)$

Multiply $- 3$ by $2$ .

$- 3 x - 6 - 1 = 1 + 2 (1 - 2 x)$

Subtract $1$ from $- 6$ .

$- 3 x - 7 = 1 + 2 (1 - 2 x)$

Simplify $1 + 2 (1 - 2 x)$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 7 = 1 + 2 \cdot 1 + 2 (- 2 x)$

Multiply $2$ by $1$ .

$- 3 x - 7 = 1 + 2 + 2 (- 2 x)$

Multiply $- 2$ by $2$ .

$- 3 x - 7 = 1 + 2 - 4 x$

Add $1$ and $2$ .

$- 3 x - 7 = 3 - 4 x$

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

Add $4 x$ to both sides of the equation.

$- 3 x - 7 + 4 x = 3$

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

$x - 7 = 3$

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

Add $7$ to both sides of the equation.

$x = 3 + 7$

Add $3$ and $7$ .

$x = 10$