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

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

$3 x + 2 x - 8 = 4 (x - 1) - x$

Add $3 x$ and $2 x$ .

$5 x - 8 = 4 (x - 1) - x$

Simplify $4 (x - 1) - x$ .

Simplify each term.

Apply the distributive property.

$5 x - 8 = 4 x + 4 \cdot - 1 - x$

Multiply $4$ by $- 1$ .

$5 x - 8 = 4 x - 4 - x$

Subtract $x$ from $4 x$ .

$5 x - 8 = 3 x - 4$

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

Subtract $3 x$ from both sides of the equation.

$5 x - 8 - 3 x = - 4$

Subtract $3 x$ from $5 x$ .

$2 x - 8 = - 4$

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

Add $8$ to both sides of the equation.

$2 x = - 4 + 8$

Add $- 4$ and $8$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$