# How do you solve \frac { 16} { x + 4} = \frac { 4} { 7}?

Sep 30, 2017

$x = 24$

#### Explanation:

$\text{one way is to use the method of "color(blue)"cross-multiplying}$

•color(white)(x)a/b=c/drArrad=bc

$\Rightarrow \frac{16}{x + 4} = \frac{4}{7} \leftarrow \textcolor{b l u e}{\text{cross-multiply}}$

$\Rightarrow 4 \left(x + 4\right) = 16 \times 7$

$\Rightarrow 4 x + 16 = 112$

$\text{subtract 16 from both sides}$

$4 x \cancel{+ 16} \cancel{- 16} = 112 - 16$

$\Rightarrow 4 x = 96$

$\text{divide both sides by } 4$

$\frac{\cancel{4} x}{\cancel{4}} = \frac{96}{4}$

$\Rightarrow x = 24$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides are equal then it is the solution.

$\frac{16}{24 + 4} = \frac{16}{28} = {\cancel{16}}^{4} / {\cancel{28}}^{7} = \frac{4}{7}$

$\Rightarrow x = 24 \text{ is the solution}$