#### Answer

The extremes are $x - 3$ and $9$. The means are $x + 4$ and $5$.
$x = 11.75$

#### Work Step by Step

A proportion takes the following form:
$\frac{a}{b} = \frac{c}{d}$, where $a$ and $d$ are the extremes and $b$ and $c$ are the means.
In this exercise, $a = x - 3$, $b = x + 4$, $c = 5$, and $d = 9$.
The extremes are $x - 3$ and $9$. The means are $x + 4$ and $5$.
Let's solve for $x$:
$\frac{x - 3}{x + 4} = \frac{5}{9}$
Use the cross products property to get rid of the fractions:
$5(x + 4) = 9(x - 3)$
Multiply to simplify:
$5x + 20 = 9x - 27$
Subtract $9x$ from each side of the equation to move variables to the left side of the equation:
$-4x + 20 = -27$
Subtract $20$ from each side of the equation to move constants to the right side of the equation:
$-4x = -47$
Divide each side by $-4$ to solve for $x$:
$x = 11.75$