Solve for x 3(x-2)-4x=2(x-9)

$3 (x - 2) - 4 x = 2 (x - 9)$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 - 4 x = 2 (x - 9)$

Multiply $3$ by $- 2$ .

$3 x - 6 - 4 x = 2 (x - 9)$

Subtract $4 x$ from $3 x$ .

$- x - 6 = 2 (x - 9)$

Step 2

Simplify $2 (x - 9)$ .

Apply the distributive property.

$- x - 6 = 2 x + 2 \cdot - 9$

Multiply $2$ by $- 9$ .

$- x - 6 = 2 x - 18$

Step 3

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

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

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

Subtract $2 x$ from $- x$ .

$- 3 x - 6 = - 18$

Step 4

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

Add $6$ to both sides of the equation.

$- 3 x = - 18 + 6$

Add $- 18$ and $6$ .

$- 3 x = - 12$

Step 5

Divide each term in $- 3 x = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 12$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 12}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$x = 4$