Solve for w -47-10w=-9w-40-3w

$- 47 - 10 w = - 9 w - 40 - 3 w$

Since $w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 9 w - 40 - 3 w = - 47 - 10 w$

Subtract $3 w$ from $- 9 w$ .

$- 12 w - 40 = - 47 - 10 w$

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

Add $10 w$ to both sides of the equation.

$- 12 w - 40 + 10 w = - 47$

Add $- 12 w$ and $10 w$ .

$- 2 w - 40 = - 47$

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

Add $40$ to both sides of the equation.

$- 2 w = - 47 + 40$

Add $- 47$ and $40$ .

$- 2 w = - 7$

Divide each term in $- 2 w = - 7$ by $- 2$ and simplify.

Divide each term in $- 2 w = - 7$ by $- 2$ .

$\frac{- 2 w}{- 2} = \frac{- 7}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 w}{- 2} = \frac{- 7}{- 2}$

Divide $w$ by $1$ .

$w = \frac{- 7}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$w = \frac{7}{2}$

The result can be shown in multiple forms.

Exact Form:

$w = \frac{7}{2}$

Decimal Form:

$w = 3.5$

Mixed Number Form:

$w = 3 \frac{1}{2}$