# make x the subject.. functions and equations

#### Sassbean19

##### New member
Hi all, I have been tasked with some practice equations to rearrange and I have been doing ok, purely because the answers are multiple choice so I try different operations in different orders until I get an answer listed...

But the fundamentals are still eluding me (maths is not my strong point to say the least).

How do I know which operations to perform to get the right answer, since it seems I could trial and error several answers for each equation which are not correct.

For example, I am struggling with the following:

Rearrange the following to make x the subject:

y=7-2x

So where am I "supposed" to start?

I have tried dividing by x first, but this leads to a seemingly dead and incorrect end (unless I'm missing something?). = y/x = 7-2

Then I tried dividing by 7 first leaving
y/7 = -2x

then multiplying by -2 to give: y/(7-2) but then I don't know if its actually (y-2)/7 = x because I don't know a rule to say whether the multiplied number moves to the top or bottom of the division on the other side, or essentially brackets the division as its own operation and acts on the whole thing: (y/7)-2 etc.

Anyway, it doesn't matter because all the above are incorrect...

I have been given the answer by the system, the above is just examples of how I am approaching this, since it worked for me in simpler questions..

x = (7 - y)/2

brackets are just to show 7 - y as being on the top half of the division line..

I have no idea how to get to the answer.. like there must be a process to lead to it that is based in something other than trial and error with operations, right? Otherwise how do you ever know you're correct? What am I missing this is driving me crazy...

Thanks all

#### banjo89

##### New member
Y = 7 - 2X
Becomes:
Y - 7 = - 2X
(It is like this: 10 = 6 + 4 so then 10 - 6 = 4)

Now multiply everything by -1 so that the X is positive
- Y + 7 = 2X

This is the same as:
7 - Y = 2X
You have 2X but want 1X so divide both sides by 2

(7 - Y) / 2 = X

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#### Jomo

##### Elite Member
y=7-2x

So where am I "supposed" to start?

I have tried dividing by x first, but this leads to a seemingly dead and incorrect end (unless I'm missing something?). = y/x = 7-2

Then I tried dividing by 7 first leaving
y/7 = -2x
I have a few comments to make and to be honest they scare me a bit.

You have y=7-2x and you want to divide by x. My concern is that you did not divide the 7 by x as well.

Consider this example 10 = 8+2 (do you agree with this equal sign?). Now I feel like dividing by 2. So I get 10/2 = 8 + 2/2. That gives us 5 = 8 +1.Do you believe that? Now consider this 10/2 = 8/2 + 2/2. That is 5 = 4 + 1. Do you believe that? You must divide (multiply) all terms!

Now you have y = 7 - 2x and you want to divide by 7. But 7/7 is 1 NOT 0 and you didn't divide the 2x by 7?. What happened to the result of 7/7??
y/7 = 7/7 - 2x/7 or y/7 = 1 -2x/7.

You need to learn to play with the numbers. If 11- 3 = 8, then 11= 8 + 3 and 3=11-8. You must get good at this. In 12+3=15 we get 15-3 = 12 and 15 - 12 = 3. These are important rules.

Now let's talk about 2x for a moment. Suppose you went to the store and bought two identical items and the total cost was $12. So you know the cost of the 2 identical items ($12). How would you figure out what one item cost? You'd divide by 2.

Now in y = 7 - 2x we want to isolate the term that has x in, namely 2x.

Now using the rules above we get 2x=7-y. Now we know exactly what 2x equals, it equals 7-y. So we divide by 2 and get x= 7/2 - y/2 or x= (7-y)/2

#### Sassbean19

##### New member
Thank you both for trying to explain.. I get the concept I'm just finding it impossible to apply, I don't think my brain works this way..

Like y = 8x(top)/5+2x(bottom)

I know I need to multiply out the 5+2x, but this is the sort of thing where I encounter issues, my fundamentals just aren't strong enough..
would it be:

y5+2x = 8x

or

5y+2x = 8x

or

y(5+2x) = 8x

whichever it is (or isn't if that's incorrect also) .. I was informed after this stage I need to "collect the x's" but I have no clue what that means..

I actually feel like crying when faced with this sort of thing, everyone else on my course seems to just be fine with it and its not because I don't try, I sit here frustrated and angry after hours sometimes of playing with the equations or other maths problems with not much success..

#### Jomo

##### Elite Member
Here we go again with patterns. If 10/2 = 5, then 10/5=2 and 5*2=10. We will use the last one, that is if 5 =10/2, then 2*5 = 10 (the bottom times the other side equals the top).

y = 8x/(5+2x). So y(5+2x) = 8x. Distribute the y--- 5y + 2xy = 8x---- 5y = 8x-2xy (now factor)----5y = x(8-2y)----now one of the rules! $$\displaystyle \frac{5y}{8-2y} = x$$ OR $$\displaystyle x = \frac{5y}{8-2y}$$