The basic idea is making one term equate to an equation. I'llg ive you a very simply one to get the idea.
2+3+6 = 3+3+5 Both sides equate to 11.
Since both sides has +3, in order to get rid of this - we minus both sides by 3 in order to get rid of them. You therfore now have -
2+6 = 3+5 which is true as both sides equate to 8. This shows that if you manipulate one side, you need to balance it out with another.
Try 2/4 = 1/2
You want to make 1 the "subject". So since on the right side, 1 is divided by 2, to get rid of this we must multiply both sides by 2 to get rid of the division.
2*2/4 = 1
4/4 = 1
1 = 1 which is true.
This application is the same for multiplication of terms, but you divide instead of multiplying.
2*4 = 2*2*2 You want to make 4 the subject. Since both sides has a *2, divide both sides by 2 in order to get rid of them.
4 = 2*2 = 4, making this statement true.
The general idea is to balance out both sides, if you add 1 to one side, you must also add it to the other.
I'll give you a straight line and try my best to go step by step as to how make a pronumeral the subject.
2x + 3y - 6 = 0
Making y the subject, we wnat to make one side only have a single y.
2x+3y = 6
In order to get rid of the -6, we need to add 6 to both sides, another way of looking at this is bringing the 6 to the right side by reversing its sign (in this case, it's -6, so we need to ADD 6 to the right side).
Since we now have 2x+3y = 6, we still want y by itself, so in order to do that we need to move the 2x to the right side. This becomes -
3y = -2x + 6 (same idea as before, in order to get rid of the 2x on the left side, we need to minus 2x from both sides to even it out)
Since we have 3y = -2x + 6 and we want y to be single (monic or singular without it being multiplied by a number), from the above example of 2*4 = 2*2*2, we need to divide both sides by 3 to make y the subject.
You then get, with y being the subject -
y = (-2x+6)/3
Sorry if it seemed all over the place, if you ahve any other enquiries i'd gladly help you out.
