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

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $3$ .

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

Multiply $2$ by $- 1$ .

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

Subtract $2 x$ from $x$ .

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

Apply the distributive property.

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $- 3$ .

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

Subtract $2 x$ from $3 x$ .

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

Step 3

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

Simplify each term.

Apply the distributive property.

$x - 6 = 2 - (3 - 2 x - 2 \cdot 1)$

Multiply $- 2$ by $1$ .

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

Subtract $2$ from $3$ .

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

Apply the distributive property.

$x - 6 = 2 - (- 2 x) - 1 \cdot 1$

Multiply $- 2$ by $- 1$ .

$x - 6 = 2 + 2 x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$x - 6 = 2 + 2 x - 1$

Subtract $1$ from $2$ .

$x - 6 = 2 x + 1$

Step 4

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

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

$x - 6 - 2 x = 1$

Subtract $2 x$ from $x$ .

$- x - 6 = 1$

Step 5

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

Add $6$ to both sides of the equation.

$- x = 1 + 6$

Add $1$ and $6$ .

$- x = 7$

Step 6

Divide each term in $- x = 7$ by $- 1$ and simplify.

Divide each term in $- x = 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$x = - 7$

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

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