The problem presents a balanced hanger diagram. On one side of the hanger, there are two $k$ values, and on the other side, there is a value of $18$. We need to find the equation that represents this balanced state and then find the value of $k$ that satisfies the equation.

1. Problem Description

The problem presents a balanced hanger diagram. On one side of the hanger, there are two $k$ values, and on the other side, there is a value of $18$. We need to find the equation that represents this balanced state and then find the value of $k$ that satisfies the equation.

2. Solution Steps

First, we need to represent the hanger diagram as an equation. The left side of the hanger has two $k$s, which can be represented as $2k$. The right side of the hanger has the value $18$. Since the hanger is balanced, the two sides are equal. Therefore, the equation is $2k = 18$.

Next, we need to solve for $k$. We have the equation:

$2k = 18$

To isolate $k$, we divide both sides of the equation by $2$:

$2k/2 = 18/2$

$k = 9$

3. Final Answer

$k = 9$