Math Is Fun Forum

mmoadi

Member

Registered: 2009-09-23

Posts: 1

Modulus inequalities

I do not know where to start! Help me, please!
I have problem finding the solution to these inequalities:

1) |x² - x| - |x| < 1
2) |x| / (x – 2)² ≥ 1
3) ||x + 1| - |x - 1|| < 1
4) (√x² + 1) + 2x – 1 > 0
5) |x² -1| + |2 - x| < 2
6) 1 + |x - 1| / 1 - |x - 1| ≤ 1

Thanks!

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Modulus inequalities

Hi mmoadi
I think that you must redefine these inequalities without using the absolute value notation , after that you deal with  usual inequaliteis  containing functions of more than one rule.
Best Wishes
Riad Zaidan

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Modulus inequalities

Hi mmoadi;

At least this one appears easy:

4)

Last edited by bobbym (2009-09-23 10:39:40)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Modulus inequalities

Hi bobbym
When taking the square root for x² you must take the absolute value of x and so you will have two inequalities, and youmust solve these two inequalities
-x+ 1+ 2x – 1 > 0 when x<0 ⇒ x>0 which is empty sunce x<0 and
x+ 1+ 2x – 1 > 0 when x>0⇒3x>0 ⇒x>0 therefore the solution of this inequality is {x∈R: x>0} mainly the positive reals.
Best Regards
Riad Zaidan

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Modulus inequalities

I think mmoadi made a slight typo in (4): I think it should be

Last edited by JaneFairfax (2009-09-24 23:34:12)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Modulus inequalities

Hi rzaidan;

That is exactly how I did it. By splitting it into 2 inequalities as you indicate.

I just did not show the work of solving the first inequality. I just did the second one.

Last edited by bobbym (2009-09-25 00:02:34)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Modulus inequalities

Never mind, forget what I said. Sorry.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Modulus inequalities

Nothing to forget. I have great respect for you.

Last edited by bobbym (2009-09-25 00:07:45)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Modulus inequalities

Thanks.

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Modulus inequalities

Thanks for all