(a-b)/-c = (a+b)/c

[errequeerre]

Hi,

I transforming a formula (5a + 7b = 4), and I get the following solution for b (b = (4 - 5a)/-7 , however, the key in the book says: (4 - 5a)/7

Is that a rule? I cannot understand why?

If anybody could help, I'd be very thankful.

Regards,

 

[pka]

I transforming a formula (5a + 7b = 4), and I get the following solution for b (b = (4 - 5a)/-7 , however, the key in the book says: (4 - 5a)/7
Is that a rule? I cannot understand why?

If you divide 35 by 7 do you get 5 or -5? Which?

So above where did you get the -7?

 

[JeffM]

Hi,

I transforming a formula (5a + 7b = 4), and I get the following solution for b (b = (4 - 5a)/-7 , however, the key in the book says: (4 - 5a)/7

Is that a rule? I cannot understand why?

If anybody could help, I'd be very thankful.

Regards,

Do NOT skip steps.

\(\displaystyle 5a + 7b = 4 \implies \)

\(\displaystyle 5a + 7b - 5a = 4 - 5a \implies\)

\(\displaystyle 7b = 4 - 5a \implies\)

\(\displaystyle \dfrac{7b}{7} = \dfrac{4 - 5a}{7} \implies\)

\(\displaystyle b = \dfrac{4 - 5a}{7}.\)

At no point is a minus 7 involved.

 

[errequeerre]

Hi, Thanks for your help.

I'm sorry, after I had spent what seems to me like hours teaking around the problem, I copied it wrongly.

The original was 5a - 7b = 4, which is why I got (4-5a)/-7

Is that right now? Is that the same as (4+5a)/7?

Thank you!

 

[pka]

I'm sorry, after I had spent what seems to me like hours teaking around the problem, I copied it wrongly.
The original was 5a - 7b = 4, which is why I got (4-5a)/-7
Is that right now? Is that the same as (4+5a)/7?

No it is not: \(\displaystyle \dfrac{4-5a}{-7}=\dfrac{5a-4}{7}\).

Do you see why?

 

[errequeerre]

I'm afraid I don't...

 

[stapel]

I'm afraid I don't...

Take a look at these:

5 - 3 = 2
3 - 5 = -2

7 - 4 = 3
4 - 7 = -3

10 - 6 = 4
6 - 10 = -4

Do you see how, when you reverse the subtraction, a "minus" sign is kicked out? Then look at these:

-2/3 = 2/(-3)

-5/4 = 5/(-4)

-7/9 = 7/(-9)

Do you see how the "minus"sign can be moved from the numerator to the denominator?

Now do ALL the steps in the fraction simplification, reversing the subtraction, kicking the "minus" sign out front, and then moving that sign underneath. What do you get?

 

[JeffM]

Hi, Thanks for your help.

I'm sorry, after I had spent what seems to me like hours teaking around the problem, I copied it wrongly.

The original was 5a - 7b = 4, which is why I got (4-5a)/-7 This is A correct answer to solving 5a - 7b = 4 for b. Another is (5a - 4)/7. The two answers mean the same thing: they are equivalents.

Is that right now? Yes. Is that the same as (4+5a)/7? No, absolutely not.

Thank you!

I said before: you must not skip steps. You also must be careful. Why do you ask about (4 + 5a)/7? That is NOT what the book says is the correct answer. Look carefully at your first post. It says the book says the correct answer is (4 - 5a)/7.

I transforming a formula (5a + 7b = 4) ... however, the key in the book says: (4 - 5a)/7

The book's answer is correct for THAT problem.

Now go back and look carefully at both the problem and the answer key. It is always possible that the answer key is wrong, but you have been jumping around writing different expressions with plus and minus signs as though they mean the same thing.

Write down the problem exactly and carefully.

Show your work carefully and in detail.

Copy the answer key's answer exactly and carefully.

Then we can figure out what is going on.

 

[errequeerre]

Hi




On a less serious note. I used Microsoft Equation to write this message, but then, when pasting, the equations did not appear, which is why I have embedded the whole text as an image. I see that some of you manage to do include equations into the message body. Is there any trick?

 

[JeffM]

First of all, I suggest you reread this post

http://www.freemathhelp.com/forum/threads/81799-Pluses-and-minuses?p=337135#post337135

If I remember correctly, we primarily discussed addition and negative numbers, not multiplication and negative numbers. So you may have additional questions now that you are dealing with multiplication.

Second, a very common trick in mathematics is to multiply a number by a clever version of 1.

\(\displaystyle a = a * 1 = a * \dfrac{b}{b} = \dfrac{ab}{b}.\)

So \(\displaystyle \dfrac{4 - 5a}{-7} = \dfrac{4 - 5a}{-7} * 1 = \dfrac{4 - 5a}{-7} * \dfrac{-1}{-1} = \dfrac{\{4(-1)\} + \{(-5a)(-1)\}}{(-7)(-1)} = \dfrac{- 4 + 5a}{7} = \dfrac{5a - 4}{7}.\)

That explains the sign reversal.

Third, it is important to remind people that you are an adult teaching yourself. That sometimes calls for a different type of answer than for a child studying in a class.

Fourth, do not worry about the language used to render math on this site unless you are going to ask a lot of questions. Just write your expressions and equation in text format as clearly as possible. There is guidance on here on how to do that.

 

[errequeerre]

Thanks, I understand it now.