Equations - Changing sides

[Igloo]

I am having trouble understanding how changing sides works. Below is an example

"Make y the subject":

Q8. M – 2y = x

This what I did:

-2y = x – m

-2y/-2 = (x – m)/-2

y = (x – m)/-2

However, the answer is showing as:

y = (m – x)/-2

I can see that the letters m and x are arranged alphabetically but this doesn’t make sense to me. 7 + 8 can be written 8 + 7 without a problem but I don’t see how 7 – 8 could be written as 8 – 7.

Thank you for your help

 

[tkhunny]

a/-2 is just kind of ugly.

a/(-2) would be better

-a/2 is equivalent and much nicer.

Likewise

-(x-m) is a little excessive.

-x + m is still kind of ugly

m - x is equivalent and avoids the hanging negative sign.

In this case, it a little about aesthetics, but mostly about ambiguity and avoiding errors. Notice how you still have "-2" in your denominator. That's not correct.

Also, switching from "M" to "m" is incorrect. Changing variable names midstream is at least bad form. It WILL lead to additional errors.

 

[JeffM]

I am having trouble understanding how changing sides works. Below is an example Everything tkhunny says above about good form is correct (although I'd personally rather err on the side of an extra set of parentheses or two than depend exclusively on conventional order of operations.) Good form prevents errors and allows your teacher and others to see easily where you are having trouble.
"Make y the subject":

Q8. M – 2y = x

This what I did:

-2y = x – m This is correct except for switching from M to m. You are doing fine.
-2y/-2 = (x – m)/-2 Still doing fine conceptually, but (-2) will prevent errors. Stringing together operators like / and - may create ambiguity.
y = (x – m)/-2 Conceptually right answer to question as posed.
However, the answer is showing as:

y = (m – x)/-2 This is NOT the answer to the question posed. Make sure you have both question and answer as written in the book. If you do, there is an error in your book as you can prove BY CHECKING the answers.
Check book: m - 2y = m + [(- 2) * (m - x)/(- 2)] = m + m - x \(\displaystyle \neq\) x unless m = 0 = x.
Check you: m - 2y = m + [(- 2) * (x - m) /(- 2)] = m + x - m = x for all m and x.

I can see that the letters m and x are arranged alphabetically but this doesn’t make sense to me. 7 + 8 can be written 8 + 7 without a problem but I don’t see how 7 – 8 could be written as 8 – 7. Order does matter with subtraction. Sometimes an error creeps into a book.

Thank you for your help You're welcome.