# How do you solve 4/(w+4)=-7?

Mar 25, 2018

$w = - \frac{32}{7}$

#### Explanation:

Our equation is essentially $\frac{4}{w + 4} = - \frac{7}{1}$, thus we can cross-multiply to solve for $w$. We get:

$- 7 \left(w + 4\right) = 4$

Distributing the $- 7$, we get:

$- 7 w - 28 = 4$

Adding $28$ to both sides, we get:

$- 7 w = 32$

Dividing both sides by $- 7$, we get:

$w = - \frac{32}{7}$

Mar 25, 2018

$w = - \frac{32}{7}$

#### Explanation:

Start by multiplying each side of the equation by $\left(w + 4\right)$

$\frac{4}{\cancel{w + 4}} \cdot \cancel{\left(w + 4\right)} = - 7 \left(w + 4\right)$

Expand the parentheses:

$4 = - 7 w - 28$

Add $7 w$ and subtract $4$ from each side:

$\cancel{4} + 7 w - \cancel{4} = - \cancel{7 w} - 28 + \cancel{7 w} - 4$

$7 w = - 32$

Divide both sides by 7:

$\frac{7 w}{7} = \frac{- 32}{7}$

$w = - \frac{32}{7}$