x+|x2||x+3|=5

Question

x+|x–2|–|x+3|=5 :yak

stolyar · Answer

Looks fine with them :banana

stolyar · Answer

You have to correctly open up moduls by using intervals—and not simply terminate them. :wink:

numlock31 · Answer

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.

skoper · Answer

true, I don't get 5 either when x=-6

stolyar · Answer

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. :oops:

HowManyToGo · Answer

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.

sparky · Answer

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.

christoph · Answer

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

sparky · Answer

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

GMAT TIGER · Answer

Agree with x = 10.

X = 0 and -6 do not work.

x+|x2||x+3|=5

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