Everyone please I beg you! I need serious help on this! How do explain this has no solutions-

I've done something very similar to this recently, and I think that it's no solutions because once simplified, the 2 sides don't equal eachother, but I'm not entirely sure how it would work for the other solution types
Answer:
see explanation
Step-by-step explanation:
Given
x + 3 = x - 15 ( subtract 3 from both sides )
x = x - 18 ( subtract x from both sides )
0 = - 18 ← not possible
This indicates the equation has no solution