We need to solve the linear equation $13.5 = 9x - 4.5$ for $x$.

1. Problem Description

We need to solve the linear equation $13.5 = 9x - 4.5$ for $x$.

2. Solution Steps

First, we add $4.5$ to both sides of the equation:

$13.5 + 4.5 = 9x - 4.5 + 4.5$

$18 = 9x$

Then, we divide both sides of the equation by $9$:

$\frac{18}{9} = \frac{9x}{9}$

$2 = x$

3. Final Answer

$x = 2$