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# x+|x–2|–|x+3|=5

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SVP
Joined: 03 Feb 2003
Posts: 1597

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30 May 2003, 04:19
1
x+|x–2|–|x+3|=5 :yak

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SVP
Joined: 03 Feb 2003
Posts: 1597

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30 May 2003, 05:39
Looks fine with them
SVP
Joined: 03 Feb 2003
Posts: 1597

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30 May 2003, 23:15
ABNY2002 wrote:
How did you get -6?

You have to correctly open up moduls by using intervals—and not simply terminate them.
Intern
Joined: 15 Apr 2003
Posts: 23

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02 Jun 2003, 08:46
When I plug in -6 back into the equation, I dont get 5.

I think only 10 works.

Can someone put -6 back into the equation and see what they get.
Manager
Joined: 25 May 2003
Posts: 54

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02 Jun 2003, 16:17
true, I don't get 5 either when x=-6
SVP
Joined: 03 Feb 2003
Posts: 1597

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02 Jun 2003, 22:24
Sorry, guys.
Tzolkin made an error and I didn't check it. The equation has the only solution 10. When we open up moduls, -6 is here but is not within an appropriate interval.
Senior Manager
Joined: 17 Apr 2005
Posts: 366
Location: India

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04 Jul 2005, 06:46
sparky wrote:
Recycling ..

I got 10 as the only soln. But in a very round about way , breaking x into intervals of x>=2 , x betwenn -3 and 2 , and x < -3.

Is there any other simpler way of doing it.

HMTG.
Director
Joined: 18 Apr 2005
Posts: 531
Location: Canuckland

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04 Jul 2005, 13:19
No,
with absolute values
first you need to break everything in intervals
then solve for each interval
if the solution falls within an interval it's valid.
VP
Joined: 30 Sep 2004
Posts: 1462
Location: Germany

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04 Jul 2005, 14:00
IMO its 0 as well. x+(-(x-2))-(-(x+3))=5 => x-x+2+x+3=5 => x+5=5 => x=0 OR x+x-2-x-3=5 => x=10
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Director
Joined: 18 Apr 2005
Posts: 531
Location: Canuckland

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04 Jul 2005, 15:00
1
stolyar wrote:
Try this one:

x+|xâ€“2|â€“|x+3|=5

let's see

(x-2) > 0 => x>2
(x+3)>0 => x>-3

so

x<-3, x - (x-2) + (x+3) = 5 => x = 0 > -3, so no solution
-3<x<2, x -(x-2) - (x+3) = 5 => x=-6 , no solution
x>2, x + (x-2) - (x+3) = 5 => x = 10, x>2 so 10 is a solution here

SVP
Joined: 29 Aug 2007
Posts: 2427

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30 Jan 2009, 15:01
stolyar wrote:
Try this one:

x+|x–2|–|x+3|=5 :yak

Agree with x = 10.

X = 0 and -6 do not work.

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Re: modul equation   [#permalink] 30 Jan 2009, 15:01
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# x+|x–2|–|x+3|=5

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