Correct order of terms when rearranging formula

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nortski

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When making x the subject of this simple formula:
y = x + 2
Why does it become x = y - 2 instead of x = -2 + y ?
Basically; how do you know which order to arrange the terms? In this example; why does the -2 go after the y and not before?
 
nortski said:
When making x the subject of this simple formula:
y = x + 2
Why does it become x = y - 2 instead of x = -2 + y ?
Basically; how do you know which order to arrange the terms? In this example; why does the -2 go after the y and not before?
Click to expand...
Mathematically - it does not matter. Both are correct.

It is a "good practice" to write the terms with variables first.
 
It really is a matter of style. Unlike Subhotosh I would put the positive term first, if there were just two terms. If both terms were positive then I would write the variable first.

The reason is when you write y-2 there is no way to miss the negative sign (using handwriting). However, if you handwrite -2+y, there is a chance that that negative sign might not be seen (for example it might seem that it is part of the equal sign).

In the end, as Subhotosh said, both ways are correct. Please do not stress out over this as it simply does not matter. Again, it is a matter of style and two people will have different styles. Develop you own style!
 
nortski said:
When making x the subject of this simple formula:
y = x + 2
Why does it become x = y - 2 instead of x = -2 + y ?
Basically; how do you know which order to arrange the terms? In this example; why does the -2 go after the y and not before?
Click to expand...
To add another opinion (though we all agree that both are "correct"):

In addition to personal style and tradition, the choice can depend on context. When you are studying polynomials, it is good to always write them in descending order for consistency. Similarly, in the context of lines, it is traditional (in my culture) to write an equation as y=mx+b, again in descending order. But for a standalone problem, Jomo's idea of avoiding negative leading terms is also good for practical reasons. So there are different reasons for different choices (and also different reasons for the same choice!).

The important thing is to know that when you look at an answer in the back of the book, that is not the only way the answer can be written. You have to learn how to recognize equivalent answers. (One advantage of using software for homework is that it can determine whether your answer is correct even if it doesn't look the same; but a disadvantage is that you don't get experience recognizing equivalent answers for yourself!)
 
Just a hint--regardless of all these opinions, it may be wise to find out which method your teacher likes, and to use that format.:unsure:
 
firemath said:
Just a hint--regardless of all these opinions, it may be wise to find out which method your teacher likes, and to use that format.:unsure:
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No, no , no!!!! I think that a student should develop their own style. Teachers should not push their styles down the student's throat.
 
But if a teacher tells a class to follow some particular style (like a style guide in an English class), then you follow it. In this case, the main reason for writing answers in a particular form is ultimately to make it easier to grade, and you want your teacher to be in a good mood ...

And it's not unreasonable to teach a class a particular style when they don't yet have the experience to judge their own style. With experience, that should loosen up.
 
I was speaking about a math teacher.

A math teacher has to show a method when they show how to solve a particular problem. Early on student's, by their choice, will not deviate by that method. However later on students should be encourage to do the problem their own way by deviating from their teacher's method.

This student who made the post is in Algebra, possibly in a college setting. I feel that it is not incorrect to let this student know that they can use their own method. This may actually be a new concept to the student. Letting them know that they can have this freedom can even give them more confidence in math.

As far as it being harder for the teacher to grade, well in post cases I will say tough, as students come first. I remember teaching linear algebra demanding that the students have the courtesy to label what rule they were trying to follow while reducing a matrix. This was good for them, so they find an error and made grading so much easier when they made a mistake, since I knew what they were trying to do. However I never told them a rigid order of how to reduce a matrix.
 
Jomo said:
This student who made the post is in Algebra, possibly in a college setting. I feel that it is not incorrect to let this student know that they can use their own method. This may actually be a new concept to the student. Letting them know that they can have this freedom can even give them more confidence in math.
Click to expand...

My comment was not about methods, but about style: forms in which answers are to be given. You're arguing against something I didn't say.

I absolutely agree that multiple methods are good, and student-discovered methods can be even better. I am upset when teachers mark students wrong for using a different method than they were taught. But that is not what we are talking about in this thread:
nortski said:
When making x the subject of this simple formula:
y = x + 2
Why does it become x = y - 2 instead of x = -2 + y ?
Basically; how do you know which order to arrange the terms? In this example; why does the -2 go after the y and not before?
Click to expand...

As we've all said, it doesn't matter at all. All I said was that if a teacher has said to write all answers in descending order, then to do otherwise would be not to follow the instructions, just as if a problem said to write an answer without negative exponents. (I would still hope the teacher would make it clear that this is not a prohibition on ever writing anything in other orders, or ever using negative exponents.) And in fact, such an instruction would help make students aware that they can change the order, from whatever they come up with to the desired form.
 
Dr.Peterson said:
My comment was not about methods, but about style: forms in which answers are to be given. You're arguing against something I didn't say.

I absolutely agree that multiple methods are good, and student-discovered methods can be even better. I am upset when teachers mark students wrong for using a different method than they were taught. But that is not what we are talking about in this thread:


As we've all said, it doesn't matter at all. All I said was that if a teacher has said to write all answers in descending order, then to do otherwise would be not to follow the instructions, just as if a problem said to write an answer without negative exponents. (I would still hope the teacher would make it clear that this is not a prohibition on ever writing anything in other orders, or ever using negative exponents.) And in fact, such an instruction would help make students aware that they can change the order, from whatever they come up with to the desired form.
Click to expand...
Dr. P said it much better than I could have--and he knew what I wanted to say. o_O
 
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