How do I justify my steps when simplifying?

You justify a step the same way you decided to go through with it:

Remember a rule, axiom, postulate, theorem, or corollary you learned

that says it's a legal thing to do.

Like if you thought of erasing one of the terms in an equation because

that would make the rest of the equation easier to work with, you would

not do that, because no book or teacher ever said that it was legal.

Or if you thought of adding 42 to both sides of an equation, you could

do that, because you learned that "If equals are added to equals, then

the results are equal". Then later, if anybody ever asked you why you

could do that, or asked you to justify your step, you'd tell them the same

statement.