# Math Help - Transferring Coefficients in equations

1. ## Transferring Coefficients in equations

Hey all,

I'm new here and I'm relearning the basic rules of algebra and I've come across a problem:

(this is the simplified equation just for demonstration purposes, I've also used an image not knowing how to represent fractions here)

1st: I thought when transferring a value from one side to the other, you had to change it from negative to positive and vice-versa. Does this rule not apply because the -91 is a coefficient?
2nd: Is it a general rule that a negative over a negative can be put positive? I've tried both 168/91 AND -168/-91 and they both give 1.85 (rounded).

Thanks for any help on this. I know this looks real simple but I've forgotten most algebra "rules". I've got so many more questions, but I guess this one is the most important for today without spamming your board.

2. ## Re: Transferring Coefficients in equations

Originally Posted by neurohype
Hey all,

I'm new here and I'm relearning the basic rules of algebra and I've come across a problem:

(this is the simplified equation just for demonstration purposes, I've also used an image not knowing how to represent fractions here)

1st: I thought when transferring a value from one side to the other, you had to change it from negative to positive and vice-versa. Does this rule not apply because the -91 is a coefficient?
2nd: Is it a general rule that a negative over a negative can be put positive? I've tried both 168/91 AND -168/-91 and they both give 1.85 (rounded).

Thanks for any help on this. I know this looks real simple but I've forgotten most algebra "rules". I've got so many more questions, but I guess this one is the most important for today without spamming your board.
1. If you want to transform an equation you have to do exactly the same on both sides of the equation without changing the "equalness".
Since you wanted to get 1x you used the the property that $\frac aa = 1, a \ne 0$. So you divided the LHS by (-91) and therefore you must divide the RHS by (-91) too.

2. If you combine two equal signs the result is positive. If you combine two unequal signs the result is negative.

3. Btw: Your result can be simplified to $x = \frac{168}{91}=\frac{7 \cdot 24}{7 \cdot 13}=\frac{24}{13}$

3. ## Re: Transferring Coefficients in equations

Originally Posted by earboth
Thanks alot! This is very appreciated.

It's great to know that the two equal signs giving a positive number is a "rule of thumb".

About the division by -91 on the RHS because it was done on the left side, I guess I must have gotten that confused with transferring say constants from one side to the other. I'm still a little confused having just jumped back into math 12 years later (other than basic math problems I deal with when programming) so I don't have all the math terms correctly either yet.

Just a last question, when you say = 1,a , what does the comma stand for? From what I can logically understand, you're listing 1 as the lowest common number because anything divided by itself is equal to 1, AND so therefore a/a could be simplified as a, is that it? I'm just confused about the comma, I just figure it stands to seperate list items.

4. ## Re: Transferring Coefficients in equations

Originally Posted by neurohype
Thanks alot! This is very appreciated.

It's great to know that the two equal signs giving a positive number is a "rule of thumb".

About the division by -91 on the RHS because it was done on the left side, I guess I must have gotten that confused with transferring say constants from one side to the other. I'm still a little confused having just jumped back into math 12 years later (other than basic math problems I deal with when programming) so I don't have all the math terms correctly either yet.

Just a last question, when you say = 1,a , what does the comma stand for? From what I can logically understand, you're listing 1 as the lowest common number because anything divided by itself is equal to 1, AND so therefore a/a could be simplified as a, is that it? I'm just confused about the comma, I just figure it stands to seperate list items.
The comma is not being used as a mathematical symbol, it's being used for its English purpose, to take a breath. He's saying that a/a = 1 provided that a is not 0.

Thanks!