Solve for x 6-3(2x-4)=2(1+x)

$6 - 3 (2 x - 4) = 2 (1 + x)$

Step 1

Simplify $6 - 3 (2 x - 4)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 3$ .

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

Multiply $- 3$ by $- 4$ .

$6 - 6 x + 12 = 2 (1 + x)$

Add $6$ and $12$ .

$- 6 x + 18 = 2 (1 + x)$

Step 2

Simplify $2 (1 + x)$ .

Apply the distributive property.

$- 6 x + 18 = 2 \cdot 1 + 2 x$

Multiply $2$ by $1$ .

$- 6 x + 18 = 2 + 2 x$

Step 3

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

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

$- 6 x + 18 - 2 x = 2$

Subtract $2 x$ from $- 6 x$ .

$- 8 x + 18 = 2$

Step 4

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

Subtract $18$ from both sides of the equation.

$- 8 x = 2 - 18$

Subtract $18$ from $2$ .

$- 8 x = - 16$

Step 5

Divide each term in $- 8 x = - 16$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 16$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 16}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 16}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 8}$

Simplify the right side.

Divide $- 16$ by $- 8$ .

$x = 2$