whenever you have an equation with one variable on both sides, you might end up with one of the following case:
1. You might end up with an inconsistent equation, therefore there is not solution. Example
x = x+3. If you subtract x on both sides, you get 0=3 which is impossible.
2. You might end up having infinite solutions. Example:
x+6 = x+6. If you subtract x on both sides you get 6 =6 which is true regardless of the value of x.
3. You might end up having only one solution. Example:
3x +2 = x +5
If you subtract x on both sides and subtract 2 on both sides, you get
2x = 3.
then if you divide by two on both sides, you find
x = 3/2. So this equation has one unique solution.