transpose a formula to make x the subject.. y=x+2

I don't understand the formula for transposition and my teacher gets frustrated when I ask for help is there an explanation for dummies.

Let's say that x = 1.

Then, y = 1 + 2 = 3, right?

Ok, let's move that '1' around...

How to do that? Subtract 1 from both sides.

y - 1 = 1 + 2 - 1

What does this give?

y - 1 = 2

It's just as if you never touched that '2' there.

Now, what, when you remove 1, gives 2? Obviously, it's 3, right?

So, y = 3

Look back now, you remember you got the value of y to be 3? Well, now you solved the value of y, through two different methods! In the first one, you calculated it, and in the second one, you' guessed it'!

This means that moving number around by doing operations to both sides of an equation (an expression with the equal sign) does not affect the equation in itself!

Another example:
now, let's say you know y, and y = 3.

Put that in the equation.
3 = x + 2

Same question, what, when added to 2 gives 3? Obviously, it's 1! You solved x using a 'guess'. But how about using calculation? You make less mistakes using calculation, especially if you get very complicated equations. Let's not look for those now, but focus on our aim, making x alone on one side, so that there are only numbers that can be calculated to obtain the value of x.

To do so, remove 2 from both sides.

3 - 2 = x + 2 - 2

Now, you see that + 2 - 2 = 0? So, x + 2 - 2 = x.

So,

3 - 2 = x

and through calculation, we find that x = 3 - 2 = 1!

Now, suppose that you didn't know any value. The same principle will apply.

y = x + 2

To make x alone on one side of the equal sign (making x the subject of the formula), remove 2 from both sides.

y - 2 = x + 2 - 2
y - 2 = x

There you are, this is the final answer for your question. :)

Now, other examples:
a + b = 3 (make a the subject of formula)

To do this remove 'b' from both sides.

a + b - b = 3 - b
a = 3 - b

There you are.

More?
m - n = 4 (make n the subject of formula)

To do this, remove m from both sides.
m - n - m = 4 - m
- n = 4 - m

Oh no! You don't have 'n' but '-n'! Don't worry, let's try something else.
Add 'n' to both sides in the original equation.
m - n + n = 4 + n
m = 4 + n

Now, continue, by removing 4 from both sides.
m - 4 = 4 + n - 4
m - 4 = n

There you are! :)

[Sorry for the lengthy post :o]

Thank you so much, that makes more sense then anyone else has explained.
How does the principle work with multiplicatin or division for example v = l x r making l the subject or v = p
-
l making p the subject.

The same way :)

v = l x r

We need to make 'l' the subject. We have l 'times' 'something'. So, you want to make l alone. The problem is, you have an 'r' there. How to make that 'move' to the other side? Since it's multiplied by r, you divide by r. Let's see:









The other one now.

This time, you want to make 'p' alone, but you have that 'l' there. Since it is a quotient (that is, what you want to remove is the denominator), multiply by l on both sides, giving:









There you are :)