Question

Please help me solve each equation:

a) 3x-2/x+4 = 0

b) 2/x-3 = 0

Answer 1

@rcatabijan, you here?

Answer 2

@hero, im here

Answer 3

Are there any parentheses missing?

Answer 4

@kc_kennylau nope, thats it thats shown

Answer 5

Sometimes parentheses are necessary when converting things from Mathematical notation to text. For example, you can't write \(\dfrac{x-2}3\) as x-2/3, but you have to add parentheses so that it becomes (x-2)/3 for ambiguity.

Answer 6

Let me ask you again, are there any parentheses missing?

Answer 7

Yes, for a) I believe that you're missing parenthesis for the top and bottom in order to convert into mathematical notations yes? (3x-2)/(x+4)=0?

Answer 8

Do you have any idea?

Answer 9

For example, if you know that A/B=0, what can we say about the value of A?

Answer 10

would we need to isolate "A" in order to get the answer?

Answer 11

Yep, that would be necessary.

Answer 12

Can I move (3x-2) to the other side? would that be the first step? >< or can I divide the like terms?

Answer 13

The first step would be to multiply both sides by the denominator.

Answer 14

3x^2-8 / x^2 + 16

Answer 15

right?

Answer 16

No, that is not correct.

Firstly, (3x-2)(x+4) is not 3x^2-8, you cannot multiply the first terms together and the last terms together and then add them up.
Secondly, (x+4)(x+4) is not x^2+16, with the exact same reason as above.
Thirdly, I was referring to the both sides of the equation when I was saying "sides".

Answer 17

Can you possibly guide me with the first question? I really don't know where to start

Answer 18

\[\begin{array}{rcl}
\frac{3x-2}{x+4}&=&0
\end{array}\]

Answer 19

Multiply both sides by x+4:
\[\begin{array}{rcl}
\frac{3x-2}{\color{blue}{x+4}}\times(\color{blue}{x+4})&=&0\times(\color{blue}{x+4})
\end{array}\]

Answer 20

What can you do now?

Answer 21

cancel x+4 on the left side, then try to isolate for "x"?

Answer 22

What do you get after cancelling?

Answer 23

3x -2 = x+4

Answer 24

How did you get the x+4 on the right hand side?

Answer 25

because of "
0×(x+4)"

Answer 26

or do you not do that?

Answer 27

cause usually when you multiply one side you do to the other as well, well thats what I learned

Answer 28

Im reading in my note that the numerator must equal zero but not the denominator.

Therefore,

3x−2
x+4 ×(x+4) = 0×(x+4)

**WIll give me:

3x-2 = 0

3x = 2

x = 2/3???

Answer 29

Please note that 0(x+4) is 0 instead of x+4. I notice that you have corrected this mistake.

Yes, your answer is perfectly correct.

Answer 30

omg thank you. One more question to go.

What if I were to do the same for the second question BUT it contains the "x".

would it be just 2 = 0? I assume this is incorrect.

Answer 31

the denominator contains the "x"

Answer 32

What you have done is perfectly correct.

Answer 33

Think about it this way. Think of (x-3) as one number. Now you have 2 divided a number equals to 0. 2 divided by what is equal to 0?

Answer 34

0?

Answer 35

2/0=0 ?!

Answer 36

That's total wrong.. would it be undefined? because my calc says error

Answer 37

Correct

Answer 38

it seemed like a tricky question..

Answer 39

I feel better now, thanks Kc, I'm going to continue on my other work and write down my stepped answers. You're a life saver

Answer 40

I'm doing MHF 4U, I may have more questions, is there any way I can contact you for more help if I need it in the future?

Answer 41

Here :)

Answer 42

Bookmarked your page so I can message you :) Thanks again! :D