The system is comprised of two processes
that go on at the same time:
#1). Do what ever you want to, to get 'x'
on one side of the equation, and
everything else on the other side.
#2). Whatever you do to one side of the equation,
you must immediately do the same thing to the
other side.
That's the system.
Here's how it works: (I can't believe you're in high school math
and you've never seen, studied, or practiced this before.)
You said that 4x - 9 = 2x + 15
and you need to find
what 'x' is.
Subtract 2x from each side: 2x - 9 = 15
Add 9 to each side: 2x = 24
Divide each side by 2 : x = 12 .