#### Answer

The extremes are $15$ and $x$. The means are $x + 2$ and $9$.
$x = 3$

#### 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, $a = 15$, $b = x + 2$, $c = 9$, and $d = x$.
The extremes are $15$ and $x$. The means are $x + 2$ and $9$.
Let's solve for $x$:
$\frac{15}{x + 2} = \frac{9}{x}$
Use the cross products property to get rid of the fractions:
$15x = 9(x + 2)$
Multiply on the right side of the equation to simplify:
$15x = 9x + 18$
Subtract $9x$ from each side of the equation to move variables to the left side of the equation:
$6x = 18$
Divide each side by $6$ to solve for $x$:
$x = 3$