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# Some modulus questions (C3) watch

1. (Original post by gangsta316)
Also does

or is that only if n is positive?
n must be positive. If n was negative, the left hand side would be negative, and the right hand side positive.
2. (Original post by royale_sufi)
I THINK that that is true since n is just a constant, regardless of the sign.
Correction... It will only work when n is positive.

Apologies for my mistake!
3. (Original post by royale_sufi)
Well, the best way to know is to learn to sketch your graphs!

With reference to the squaring both sides method... do you think you would be able to solve the following EQUALITY with that method?

|(x^2) + 4x| = |3(x^2) + 2|

The problem with squaring both sides is that you may generate extra solutions that arent neccessarily true.
Maybe but I've yet to come across an x^2 in the mod brackets with one like that.
4. (Original post by gangsta316)
How do you draw these graphs?

. Is it just - actually I see that it's not because x = 0 doesn't work.

Also

They are in my textbook as OCR questions but they are starred meaning they are more difficult. Maybe it means that they're old and no longer on the syllabus.
For drawing those graphs, the only method i am aware of is plotting... i.e finding what y is at x=0 and what y is at x=1 and what y is at x=-1 etc.

Any other ways anyone else is aware of?
5. So if n is negative you could say

6. (Original post by gangsta316)
Maybe but I've yet to come across an x^2 in the mod brackets with one like that.
i doubt you would be able to solve it as it will be a quartic graph once you square it with a term in x^3 which is extremely difficult to solve.
7. (Original post by royale_sufi)
For drawing those graphs, the only method i am aware of is plotting... i.e finding what y is at x=0 and what y is at x=1 and what y is at x=-1 etc.

Any other ways anyone else is aware of?
Never plot! You could consider what happens in the different regions between the critical values of x (i.e. x<-3 -3<x<3 x>3).
8. (Original post by royale_sufi)
i doubt you would be able to solve it as it will be a quartic graph once you square it with a term in x^3 which is extremely difficult to solve.
And so the answer is: do not square. Sketchhhh.
9. (Original post by Daniel Freedman)
Never plot! You could consider what happens in the different regions between the critical values of x (i.e. x<-3 -3<x<3 x>3).
Thats a nice way. Plotting would do pretty much the same thing though
10. (Original post by royale_sufi)
Thats a nice way. Plotting would do pretty much the same thing though
Yes, but it's ugly and takes too long.
11. (Original post by Daniel Freedman)
Yes, but it's ugly and takes too long.
Well its a good starting place for people who arent comfortable with sketching graphs... i think we all learnt to plot before sketch!
12. Ok so I'll square but I'll plot when there's an x^2 involved.

Does squaring work when only one side has mod brackets? It definitely always works when both sides are in mod brackets (with no minus before the mod) because my book says so.

EDIT:

I found that squaring isn't always good. It only works when both sides have mod brackets. If only one side has mod brackets squaring can create more, incorrect solutions. Like with these

and

I still think that, when you have solving two separately with and is better than sketching.

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