Solve for w 3w+4-w=5w-2(w-2)

$3 w + 4 - w = 5 w - 2 (w - 2)$

Step 1

Subtract $w$ from $3 w$ .

$2 w + 4 = 5 w - 2 (w - 2)$

Step 2

Simplify $5 w - 2 (w - 2)$ .

Simplify each term.

Apply the distributive property.

$2 w + 4 = 5 w - 2 w - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$2 w + 4 = 5 w - 2 w + 4$

Subtract $2 w$ from $5 w$ .

$2 w + 4 = 3 w + 4$

Step 3

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

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

$2 w + 4 - 3 w = 4$

Subtract $3 w$ from $2 w$ .

$- w + 4 = 4$

Step 4

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

Subtract $4$ from both sides of the equation.

$- w = 4 - 4$

Subtract $4$ from $4$ .

$- w = 0$

Step 5

Divide each term in $- w = 0$ by $- 1$ and simplify.

Divide each term in $- w = 0$ by $- 1$ .

$\frac{- w}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{0}{- 1}$

Divide $w$ by $1$ .

$w = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$w = 0$