not so easy equation

Question

Solve the following double-modul equation: :scared 

||X|–1|=1

omar_far · Answer

Can someone please explain me how to solve modul equations? I would really appreciate it. :cry:

ruhi · Answer

Time taken:30 secs.

squaring both sides, (|x|-1)^2=1
|x|^2-2|x|=0
if x>0,

x^2-2x=0 
x=0 or 2

if x<0
x^2+2x=0
x=0 or -2

final ans: -2,0,+2.

revital · Answer

another way 

|| means it can be positive or negative 
we will check all the options

|x-1|=1 or |-x-1|=1
this can be divided to another 4 options 

x-1=1
x-1=-1
-x-1=1
-x-1=-1

solve it and you will get -2 2 and 0

gmat1obsessed · Answer

0,2,-2.........

Here how I solved ..........


||x|-1| = 1 it gives 2 equations :

+(|x| - 1) = 1 => x =2,-2

-(|x| -1) =1 => x=0

jinino · Answer

My tip for absolute question is to remember the number inside the absolute bracket can be either positive or negative. i.e. |x|=2, x can be either +5 or -5 Hope this helps! :beer

omar_far · Answer

Thank you all for the help. Wow there are a lot of ways to solve this. Let me try my new-found knowledge to other modul problems on the forum. Thanks again.

praveen_rao7 · Answer

I did it this way

split the equation
|X-1| = 1
|-X-1| =1

now, plug the values for X that makes sense

you get 2 , 0 , -2

I like Ruhi's method too.

ian7777 · Answer

same answer as everyone else.

With absolute value, I always rewrite the equation twice, the second time with the answer negative (as opposed to the other approach which is to make the number in the absolute value negative). That just works better for me.

So I got these two equations:

|x|-1 = 1 and |x|-1 = -1
|x| = 2 and |x| = 0
x = 2 or -2 and x = 0

not so easy equation

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