Because there is no charge, the charge should add up to zero.
We know Oxygen always has an oxidation number of -2, however in this case there are 3 oxygen atoms. We know there are three oxygen atoms because it has the subscript of 3.
So 3x-2= -6
We also know the charge of Hydrogen (H) is always +1, there is only 1 hydrogen atom.
From here we can set up an equation to solve for Nitrogen, because we know it should add up to 0
So our equation is
H+O3+N=0
Next we plug in our values
1+-6+x=0
Then we solve for x by isolating it
So first subtract -6 from both sides
The equation is now 1+x=6
Then we'll subtract 1 from each side, leaving the equation as
x=5
So the oxidation number of N is +5
