How to solve a greatest integer equation for $x$? This is a greatest integer equation. Solve for $x$:
$$
[2x-7]=-3
$$

It's easy friend. 
Firstly you should keep in mind that $x= [x] + \{x\}$ and $0 \leq \{x\}<1$ 
So, $2x-7 - \{2x-7\}=-3$ 
$\implies 2x-4 = \{2x-7\}$ 
$\implies 0 \leq (2x-4)<1$ 
$\implies 2 \leq x < 2.5 \implies x \in [2, 2.5)$
another equivalent method, $[2x -7] = [2x] -7 = -3 \implies [2x] = 4$ 
$\implies 2x - \{2x\} = 4 \implies 2x -4 = \{2x\}$ and you can solve as before. 
In case, in the question $x \in \mathbb{N}$ then you get $x=2$.
