Inequation

[Loki123]

So I would say that x is lower or equal to 6, but in the answer sheet it say just lower than 6. This makes sense because if we say 6-sqrt(x) =0 we get sqrt(x) <0, which I don't think is correct. But I would usually use higher or equal to or lower or equal to. for these provlems. Am I correct in ky thinking. Thanks

 

[Dr.Peterson]

So I would say that x is lower or equal to 6, but in the answer sheet it say just lower than 6. This makes sense because if we say 6-sqrt(x) =0 we get sqrt(x) <0, which I don't think is correct. But I would usually use higher or equal to or lower or equal to. for these provlems. Am I correct in ky thinking. ThanksView attachment 32756

What are you saying is the solution to the inequality? It definitely is not either [imath]x<6[/imath] or [imath]x\le 6[/imath]!

Are you just referring to one step of the work??

 

[Loki123]

What are you saying is the solution to the inequality? It definitely is not either [imath]x<6[/imath] or [imath]x\le 6[/imath]!

Are you just referring to one step of the work??

just this condition/restriction step

 

[Steven G]

...continue

 

[Steven G]

You really should know that if 6-x>0, then x<6. If you take away more than 6 from 6, you get a negative value.

Why not also state that x>= 0 for the sqrt(6) part?

 

[Steven G]

if we say 6-sqrt(x) =0 we get sqrt(x) <0

If 6-sqrt(x) = 0, then sqrt(x) = 6. How do you get sqrt(x) < 0?

 

[Dr.Peterson]

just this condition/restriction step

If you're asking why someone else said something different from you at one step in a process, you need to show the entire work for context, both yours and theirs.

You do know, I hope, that the same correct outcome can be obtained, correctly, by different methods, right? So what both of you are doing may be correct. We can only know that (or not) when we see the whole thing.

But as Steven just pointed out, at least one part of what you say is incorrect.

 

[Cubist]

@Loki123 some context would definitely be useful

I suspect that the exercise is to perform a quick (and dirty) simplification of a given inequality where it doesn't matter if some tightness is lost. For example, if x<6.433635 then it's also true that x<7 (however x<7 obviously doesn't imply x<6.433635)

But I might be wrong. Please let us know.

 

[Loki123]

If you're asking why someone else said something different from you at one step in a process, you need to show the entire work for context, both yours and theirs.

You do know, I hope, that the same correct outcome can be obtained, correctly, by different methods, right? So what both of you are doing may be correct. We can only know that (or not) when we see the whole thing.

But as Steven just pointed out, at least one part of what you say is incorrect.

Here:

The way I solved it is the way I always solve problems like these. However this made me question something.
Basically if I have
sqrt(a) <b,
I would say b>=0,
however, if b=0, we would get
sqrt(a)<0
which can't be true bc sqrt is always postitive, right?

 

[Steven G]

I agree that it should say that x < 6

 

[pka]

Here:
View attachment 32758
The way I solved it is the way I always solve problems like these. However this made me question something.
Basically if I have sqrt(a) <b, would say b>=0, however, if b=0, we would get sqrt(a)<0
which can't be true bc sqrt is always postitive, right?

I agree that it should say that x < 6

Let us be vary clear as to the exact question: [imath]\large \sqrt{x}<6-x[/imath]. If so proceed.
[imath]x+\sqrt{x}-6<0\\(\sqrt{x}-2)(\sqrt{x}+3)<0\\0\le x<4[/imath]

 

[Loki123]

Let us be vary clear as to the exact question: [imath]\large \sqrt{x}<6-x[/imath]. If so proceed.
[imath]x+\sqrt{x}-6<0\\(\sqrt{x}-2)(\sqrt{x}+3)<0\\0\le x<4[/imath]

i am not confused how it should be solved

 

[Dr.Peterson]

Here:
View attachment 32758
The way I solved it is the way I always solve problems like these. However this made me question something.
Basically if I have
sqrt(a) <b,
I would say b>=0,
however, if b=0, we would get
sqrt(a)<0
which can't be true bc sqrt is always postitive, right?

I can see reasons for both choices at that point in the work; and I don't see that it makes any difference. Why worry about this small difference?