Question

Is this B

Answer 1

Are you sure =) , need a positive answer

Answer 2

@zarkam21
Would you want to be able to solve this kind of problems by yourself?
If you do, you need to put efforts into understanding how to find the correct answer.
Would you like to do that?

Answer 3

@tshimp0629
I don't consider anyone is smarter than another. Knowledge is the same for everyone, even though the time and effort to acquire it may differ from one individual to another.
Anyone who has the will to acquire knowledge will be proficient, given enough time and effort.

Answer 4

@tshimp0629
I think you will be able to do as well.
What's important is to explain, guide her into understand how to find the correct answer, and how to check. It is important for anyone in the learning process to avoid stopping at the answer, and not worry about how.
I am sure you are able to explain to her how you found your answer so that she will have the confidence to check the next problem on her own.

Answer 5

@zarkam21
Are you ready to understand how to find the answer to this question?

Answer 6

I understand and I never said that I don't want to learn :/

Answer 7

I know the first step is
-3-x+9>0

Answer 8

Good!
Can you explain to me how you chose the answer:
"all numbers greater than or equal to -3" ?

Answer 9

Try substituting x=-3. What value does -3-x now take on?

Answer 10

That's a very good start!
However, can you tell me what is needed to be >0, and why?

Answer 11

Equal to sign but I don't think I know the reason

Answer 12

* \(\ge\)

Answer 13

Ok, now that's where it's bothering you.
The reason we need to have -3-x \(\ge\) 0 is because the expression -3-x is inside the square-root sign.

Answer 14

Unless we work with complex numbers, we are not allowed to take the square-root of negative numbers, right?

Answer 15

Oh right, so if something is inside the square root sign, it would be plain >

Answer 16

No, zero \(is\) allowed inside the square root sign, but not negative values.

Answer 17

That is why the condition -3-x\(\ge\) 0.

Answer 18

Actually, whatever is underneath the sqrt operator CAN be zero or greater. Thus, you are to solve the inequality\[-x-3\ge 0\]

Answer 19

So any x that does not satisfy this condition is not in the domain, that's is the first step in finding the answer, which is -3-x\(\ge\)0.

Answer 20

Or in other words, the domain is governed by the condition
\(-3-x\ge 0\)

Answer 21

In other words, please solve \[-3-x \ge 0~ now.\]

Answer 22

@mathmale
Since we are going in parallel, I will leave @zarkam21 in good hands!

Answer 23

\[-x \ge 3\]

Answer 24

and then \[x \le -3\]

Answer 25

@mathmale

Answer 26

@mathmale please come back

Answer 27

\[x \le -3\] looks good. We need to verify that this is correct, however.

First, let x=-3. What will the quantitiy under the radical sign then equal? Is that result acceptable?

Answer 28

Yes it is acceptable

Answer 29

@triciaal help :/

Answer 30

@steve816