Rearranging

One rule, applied repeatedly.

Balance

An equation is a balance. Do the same thing to both sides and it stays true, which is the only rule you need for solving.

Undo operations in reverse order: addition before multiplication when isolating.
Check by putting the answer back into the original equation.

Dividing by a variable can destroy a solution, because that variable might be zero. Move everything to one side and factorise instead.