Solve for w 15-2w-2=2(w-15)-1

$15 - 2 w - 2 = 2 (w - 15) - 1$

Step 1

Subtract $2$ from $15$ .

$- 2 w + 13 = 2 (w - 15) - 1$

Step 2

Simplify $2 (w - 15) - 1$ .

Simplify each term.

Apply the distributive property.

$- 2 w + 13 = 2 w + 2 \cdot - 15 - 1$

Multiply $2$ by $- 15$ .

$- 2 w + 13 = 2 w - 30 - 1$

Subtract $1$ from $- 30$ .

$- 2 w + 13 = 2 w - 31$

Step 3

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

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

$- 2 w + 13 - 2 w = - 31$

Subtract $2 w$ from $- 2 w$ .

$- 4 w + 13 = - 31$

Step 4

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

Subtract $13$ from both sides of the equation.

$- 4 w = - 31 - 13$

Subtract $13$ from $- 31$ .

$- 4 w = - 44$

Step 5

Divide each term in $- 4 w = - 44$ by $- 4$ and simplify.

Divide each term in $- 4 w = - 44$ by $- 4$ .

$\frac{- 4 w}{- 4} = \frac{- 44}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 w}{- 4} = \frac{- 44}{- 4}$

Divide $w$ by $1$ .

$w = \frac{- 44}{- 4}$

Simplify the right side.

Divide $- 44$ by $- 4$ .

$w = 11$