The key here, as with any problem, is maintaining the integrity of the equality. Basically what you do to one side you
MUST do to the other to keep them equal. Yes the problem changes but the fact that they are equal remains. This is the key to keeping the equation balanced, just like a balance scale.
Example: You and brother have $5 each. Money wise You = Brother
If I give $5 to your brother, what are you going to say? => Where's my $5
You are no longer equal, money wise. So to keep you both equal I MUST give $5 to you as well.
The money that you each have is not an issue that fact that you have the same amout is the key to keeping balance.
Expressed as an equation: let Y =Your original $5 and X - Brother's original $5
adding $5 to each side gives
both sides are equal. The equation is balanced.
It does not matter if you are adding, subtracting, multiplying or dividing,
What you do to one side of the equation you must to the other side. It is a simple as that.
In the above answer b was subtracted from both sides.
Leaving P-b = a+b+c-b
Since we can add in any order, we combine and simplify.
the (b-b)=0 and drops from the right side because adding zero does not change anything.
Next c was subtracted from both sides.
Again c-c=0 and it drops from the right side.
Rewriting since we are solving for a