Question

Solve the proportion 2 times x all over 6 times x plus 7 equals 2 over x. What is the value of x?

Answer 1

\[2x/(6x +7) =2/x\]

Answer 2

Like this?

Answer 3

Yes. So would you cross multiply 2(6x+7) then divide by 2x? I am kinda lost. :(
the possible answers are
a. x=1 and x=-7
b. x=-1 and x=7
c. x=-1 and x=6
d. x=1 and x=6

Answer 4

Actually since they equal each other then if you subtract one from the other you would get 0

Answer 5

\[(2x/(6x+7 ) - 2/x = 0\]

Answer 6

Then you need to find the least common denominator and subtract..what do you come up with?

Answer 7

2x?

Answer 8

(6x+7)(x) is the least common denominator. Multiply it back into your two numbers and what equation do you get?

Answer 9

So the least common denominator is x or (6x+7)(x)?

Answer 10

I am sorry I am having a really hard time with this problem.

Answer 11

(6x+7)(x)..do you see how a got that. When dealing with fraction that ust be added or subtracted they must have the same denominator. Most all the time the LCD (Least common denominator is multiplying the two denominators together.
Now you must multiply each number by the LCD. What will your equation look like now?

Answer 12

\[ \frac{ 2x }{ 6x+7} - \frac{ 2 }{ x } = 0\] Do you see how we got this?

Answer 13

Yes I got it so far

Answer 14

You subtracted 2/x from both sides to get a 0 on the right and a -2/x on the left

Answer 15

If a =b then a-b will always be 0.

Answer 16

Can you solve these

Answer 17

Ok take your time

Answer 18

Do any of these cancel out?

Answer 19

Yes very good..go on

Answer 20

so the top one would be 2x/x because the 6x+7 cancel right? And the bottom would be 12x+14 and the x would cancel? Am I even close?

Answer 21

The top one is (2x)(x) which equals what? The bottom one is correct very good

Answer 22

\[2x ^{2}\]

Answer 23

Now what do you do?

Answer 24

reduce?

Answer 25

Remember we were subtracting one from the other to get 0. So we subtract 2x^2 -(12x+14) and this all needs to be over our LCD. So what do we have?

Answer 26

NO idea, I am lost now.

Answer 27

What would this look like when you subtract?\[2x ^{2} -(12x+14)\]

Answer 28

Factor it?
\[2(x ^{2}-6x+7)\]

Answer 29

Close...you a\[2x ^{2}-12x-14\]re a step ahead of me...The equation would look like this

Answer 30

You see how I got that?

Answer 31

ok so then it would be a -7 instead of a +7 like I put it

Answer 32

That's right

Answer 33

2(x-7)(x+1)

Answer 34

So our equation will look like this.
\[\frac{ 2x ^{2}-12x-14 }{ (6x+7)(x)} = 0\]

Answer 35

ok Not sure what to do next

Answer 36

Factored it would look like this
\[\frac{ (2)(x-7)(x+1) }{ (6x+7)(x) } =0\]

Answer 37

Do you see this?

Answer 38

Okay that is what I did above. Yay me!

Answer 39

You are doing great...Now for a fraction to equal 0 what would it look like?

Answer 40

Still not sure where to go from here The bottom part of the fraction is throwing me off

Answer 41

The bottom is unimportant since we are only looking to find solutions that equal zero..

Answer 42

No idea what a fraction equal to 0 would look like

Answer 43

0 = 0

Answer 44

0/a =0, where a = any number
This means zero over any number will always equal 0
0/4 = 0
0/12 - 0
0/5000 =0

Answer 45

Still lost

Answer 46

What are we trying to get our factored fraction to equal??

Answer 47

0?

Answer 48

Right..so to do this we have to get the numerator (The top of the fraction to equal 0) because 0 over any number equals 0. Do you see where I am going?

Answer 49

No I don't see where you are going. I am sorry. :(

Answer 50

Not a problem..is it the concept of 0/4 or 0/8 you do not understand?

Answer 51

I understand that both those = 0. I just don't understand the next steps and what we are trying to do to find what x equals.

Answer 52

Ok so we now have to get the numerator to equal 0. Our factored numerator is
\[(2)(x-7)(x+1)\]

Answer 53

How or what can we make the values of x to make this equal 0?

Answer 54

The opposite of what they already are?

Answer 55

What happens if I make x=7?

Answer 56

How did you make x=7?

Answer 57

Remember we are trying to make the numerator = 0.
Our numerator is (2)(x-7)(x+1)
So we are trying to solve the following equation..
2(x-7)(x+1) = 0. How would you solve for x?

Answer 58

Remember 0 multiplied by any number always equals zero.
5 x 0 = 0
6 x 0 = 0
7 x 5 x 0 = 0

Answer 59

No idea

Answer 60

If (2) times (x-7) times (x+1) = 0....What happens when I make x =7?
It becomes (2) times (7-7) times (7+1) =0
Or (2) times 0 times 8 which equals??

Answer 61

0

Answer 62

So the answer must be b because that is the only one with a 7 in it.

Answer 63

Right,,When dealing with quadratic equations that equal 0. All you need to do is solve for each value of x so that the factor is 0. Your two factors are (x-7) and (x+1). So once you solve for these two unkowns you have your answer.

Answer 64

Your answers is 7 and -1.

Answer 65

Trust me this get easier with practice...

Answer 66

Thank you, I am sure I will be back soon. :)

Answer 67

You did well..

Answer 68

LOL! you are too nice. An hour later and I barely understand it. Thanks for being so patient.