Question

Help again .-. This stuff confuses me.
https://prnt.sc/faydfy

I think its no solution
My work below
-3 : 3/3(-3) + 1/-3+4 = 10/7(-3)
3/-9 + 1/1 = 10/-21
4/-8 = 10/-21

3: 3/3(3) + 1/3+4 = 10/7(3)
3/9 + 1/7 = 10/-21
4/16=10/21

-3,3 : 3/3(-3) + 1/-3+4 = 10/7(3)
3/-9 + 1/1 = 10/21
4/8 = 10/21

Answer 1

It would be much easier if we just solve for the variable.

Answer 2

@PuppyFlower, do you think you might be able to hit that equation button and type out your work?

Answer 3

3: 3/3(3) + 1/3+4 = 10/7(3)
( we can reduce 3/9 to 1/3) 3/9 + 1/7 = `10/-21` ( 3 is positive )
4/16=10/21
1/3+1/7=?

Answer 4

Doing so creates nice equations like this:
\(\dfrac{3}{3x} + \dfrac{1}{x + 4} = \dfrac{10}{7x}\)

Answer 5

For 3rd option: x=-3 , x=3 means both are solution
if you plug in the x value one at a time\[\rm (for~x=-3)~\rightarrow ~\frac{ 3 }{ 3(\color{Red}{-3}) } +\frac{1}{\color{red}{-3}+4} = \frac{10}{7(\color{Red}{-3})}\]
\[\rm (for~x=3)~\rightarrow ~\frac{ 3 }{ 3(\color{Red}{3}) } +\frac{1}{\color{red}{3}+4} = \frac{10}{7(\color{Red}{3})}\]

Answer 6

in other words.. IF you replace the variable x with 3 on left side then you have to replace the variable x with the same number 3 on the right side.

Answer 7

I know, I just get confused at the end when I have to pick an answer then I don't understand it

Answer 8

OH, I get it now lol, you don't use both -3 and 3 in the same equation, if they both give you the right answer then it would be both

Answer 9

It's better to assume they did not give you the correct variables and just do the following:
\(\dfrac{3}{3x} + \dfrac{1}{x + 4} = \dfrac{10}{7x}\)
\(\dfrac{1}{x} + \dfrac{1}{x + 4} = \dfrac{10}{7x}\)
\(\dfrac{7}{7x} + \dfrac{1}{x + 4} = \dfrac{10}{7x}\)
\(\dfrac{1}{x + 4} = \dfrac{10}{7x} - \dfrac{7}{7x}\)
\(\dfrac{1}{x + 4} = \dfrac{10 - 7}{7x}\)
\(\dfrac{1}{x + 4} = \dfrac{3}{7x}\)

Cross Multiply to get:
\(7x = 3(x + 4)\)

Then distribute to get
\(7x = 3x + 12\)

Then put like terms on the same side to get:
\(7x - 3x = 12\)

Then simplify to get:
\(4x = 12\)

Then divide both sides by 4 to isolate \(x\)

Answer 10

I'm sorry but you just made everything harder for me. I'm guessing the answer is both.

Answer 11

The answer is NOT both

Answer 12

the way you were trying to find the answer is harder/tedious than solving for the variable.

Answer 13

I'm not saying it's wrong.

Answer 14

I'm not a fan of these multiple choice questions. It only encourages the student to do things the wrong way.

Answer 15

yeah especially not for math. I remember when I Used to solve each question step by step on the final exam. No multiple choice questions...not even for bio/chem/phy exams.

Answer 16

3/3(-3) + 1/-3+4 = 10/7(-3)
`3/-9 + 1/1` = 10/-21
4/-8 = 10/-21
\[-\frac{ 3 }{ 9 } +1=-\frac{10}{21}\]
3/9=1/3
\[-\frac{1 }{ 3 } +1=-\frac{10}{21}\]
(-1/3)+1 isn't equal to -4/8

Answer 17

`3/3(3) + 1/3+4 = 10/7(3)
3/9 + 1/7 = 10/-21
4/16=10/21`
same mistake here
1/3+1/7 isn't equal to 4/16

Answer 18

` 3/3(3) + 1/3+4 = 10/7(3)`
`3/9 + 1/7 = 10/-21`
`4/16=10/21 `
same mistake here
1/3+1/7 isn't equal to 4/16