Solve for x 2x+4(3-2x)=3(2x+2)/6+4

$2 x + 4 (3 - 2 x) = 3 \frac{2 x + 2}{6} + 4$

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

Simplify each term.

Apply the distributive property.

$2 x + 4 \cdot 3 + 4 (- 2 x) = 3 (\frac{2 x + 2}{6}) + 4$

Multiply $4$ by $3$ .

$2 x + 12 + 4 (- 2 x) = 3 (\frac{2 x + 2}{6}) + 4$

Multiply $- 2$ by $4$ .

$2 x + 12 - 8 x = 3 (\frac{2 x + 2}{6}) + 4$

Subtract $8 x$ from $2 x$ .

$- 6 x + 12 = 3 (\frac{2 x + 2}{6}) + 4$

Simplify $3 (\frac{2 x + 2}{6}) + 4$ .

Simplify each term.

Factor $2$ out of $2 x + 2$ .

Factor $2$ out of $2 x$ .

$- 6 x + 12 = 3 \frac{2 (x) + 2}{6} + 4$

Factor $2$ out of $2$ .

$- 6 x + 12 = 3 \frac{2 (x) + 2 (1)}{6} + 4$

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

$- 6 x + 12 = 3 \frac{2 (x + 1)}{6} + 4$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$- 6 x + 12 = 3 \frac{2 (x + 1)}{3 (2)} + 4$

Cancel the common factor.

$- 6 x + 12 = 3 \frac{2 (x + 1)}{3 \cdot 2} + 4$

Rewrite the expression.

$- 6 x + 12 = \frac{2 (x + 1)}{2} + 4$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 x + 12 = \frac{2 (x + 1)}{2} + 4$

Divide $x + 1$ by $1$ .

$- 6 x + 12 = x + 1 + 4$

Add $1$ and $4$ .

$- 6 x + 12 = x + 5$

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

Subtract $x$ from both sides of the equation.

$- 6 x + 12 - x = 5$

Subtract $x$ from $- 6 x$ .

$- 7 x + 12 = 5$

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

Subtract $12$ from both sides of the equation.

$- 7 x = 5 - 12$

Subtract $12$ from $5$ .

$- 7 x = - 7$

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

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

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

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 7$ by $- 7$ .

$x = 1$

Solve for x 2x+4(3-2x)=3(2x+2)/6+4

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