Math for game developing quiz 6 question 1

[Dakiller]

Hi all just wondering if someone can help me understand this little bit so we have

14a + 2(3b +5) = 30 need to make a the subject

So

30 - 2(3b + 5) = 14 a /2 to get

7a = 15 - (3b + 5) expand brackets to get

7a = 15 - 3b - 5 which I get now this is where I am confused when we group these like terms we get

7a = -3b + 10

What I can’t figure out is why we don’t get 10 - 3b or
-3b - 10

Appreciate any help you guys can give I’m close just can’t wrap my head around this little part

[garypettie]

Hi @Dakiller,
-3b + 10 is exactly the same as 10 - 3b. All we’ve done is swapped the order of the terms.
You can think of subtraction as just adding a negative number, and the commutative property of addition tells us that a + b = b + a, or a + (-b) = (-b) + a.

As to why we changed the order in the first place, it’s really just a convention that we place higher order terms first. So, you might rearrange something like x + 3 + x² to read x² + x + 3.
This isn’t essential but it does tend to make more complex equations easier to work with.

I hope that helps answer your question.

[Jens]

But - 3b - 10 is not possible.

Intermediate term:
7a = 15 - 3b - 5
If you move the 15 on the right side of the equation the sign will not change.
Written with all signs the term would be:
+7a = +15 - 3b - 5
But usually a leading + sign is not written.
So you could rewrite the term:
7a = -3b + 15 - 5
that would result in 7a = -3b + 10