# B Confusion over transposing formulae question

1. Nov 14, 2016

### Buggsy GC

Hello I'm working through transposing formulae of pearsons Anthony Croft and Robert Davidson's foundation maths 5th edition and I'm stuck on exercise 10.1 question 1)e)
We're it states that I must transpose the formula to make x the subject.
The formula is y = ¹/₂x and the answer x = ¹/₂y
I don't understand how they got this answer. As I did the working as
E)y = 1/2x
× 2
(2)(y) = ⁽¹⁾/₍₂₎x × ⁽²⁾/₍₁₎
2y = x
I base this way of a working off another question which I got correct
D)y = (¹)/(₂)(x - 7)
+ 7
y + 7 = ¹/₂x
× 2
(2)(y + 7) = ⁽¹⁾/₍₂₎x × ⁽²⁾/₍₁₎
2y + 14 = x
x = 2y + 14
If I am missing some rule that I'm meant to implement or if there is a error in the textbook your advise would be greatly appreciated.
Yours sincerely Buggsy

2. Nov 14, 2016

### Staff: Mentor

That is correct.
That step is incorrect at the right side.

Try x=7 and see if you can find a value for y such that both the initial and the final formula are right.
That does not make sense.

3. Nov 14, 2016

### PeroK

If $y = \frac{1}{2x}$ then $x = \frac{1}{2y}$ is correct.

Try $x = 1$ for example.

4. Nov 14, 2016

### Staff: Mentor

I didn't expect x and y to be in the denominator.

5. Nov 14, 2016

### Buggsy GC

I know but look

6. Nov 14, 2016

### Buggsy GC

Pardon me Perok can you take a picture of your working and post it, for some reason your post shows up on my screen as a bunch of hashtags and letters.
Thank you

7. Nov 14, 2016

### PeroK

I'm sorry to tell you I did it in my head!

8. Nov 14, 2016

### PeroK

Hint: multiply by $x$ to start.

9. Nov 14, 2016

### Buggsy GC

So it look like this View attachment 108916
Ok second question how did you know to start with x not to just repeat the same action I used to get rid of the 1/2x in question d)
We're the answer was x =2y + 14 were the original formula was y = ¹/₂x - 7

10. Nov 14, 2016

### PeroK

That last equation is very different. That is

$y = \frac{x}{2} - 7$

11. Nov 14, 2016

### Buggsy GC

I'm sorry this taking a while but can tell me is there a rule I should remember or an order of operation when rearranging formulas as I' m getting different answers depending on how I start to balance the equation even if I balance both sides all the way through

12. Nov 15, 2016

### Staff: Mentor

13. Nov 15, 2016

### Buggsy GC

Question e) and d) 10.1

14. Nov 15, 2016

### PeroK

That simply means you are making a mistake. There are no rules except you can: a) add the same thing to both sides of the equation; or, b) multiply both sides of the equation by the same thing. That same thing can be a number, such as $2$ a parameter, such as $a$, or a variable, such as $x$.

For example:

$y = ax + b$

$y-b = ax$ (added $-b$ to both sides, which is the same thing as subtracting $b$)

$\frac{y-b}{a} = x$ (multiplied both sides by $\frac{1}{a}$, which is the same as dividing by $a$)

Another example is:

$y = \frac{1}{x}$

$xy = 1$ (muliplied both sides by $x$)

$x = \frac{1}{y}$ (divided both sides by $y$)

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