In a small town, the mayor is planning to reduce the speed limit on Main Street to improve safety. The current speed limit is set at $55$ miles per hour (mph). The mayor's goal is to reduce the speed limit by $x$ mph, where $x$ can be any positive integer.
The new speed limit, $L$, will be represented by the equation:
$$ L = 55 - x $$
If the mayor decides to set the new speed limit at $45$ mph, what value of $x$ represents the speed limit reduction?
Provide your answer as a decimal or a fraction in the grid-in response box.