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April 19th, 2012, 07:21 AM   #1
Ter
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Changing the range of mod x

Hellow, I have two solutions and am not sure which is right.

Let's say I have substituted a for |x|
And I solved a to be -2<a<2.
Changing it back to modulus x,
-2<|x|<2
Since mod cannot be negative,
0<x<2
My problem is, I have answers which tell me that it will be 0<|x|<2 and another tells me that I have to add 2, thus 0<x+2<4.

Which is right? Thank you.
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April 19th, 2012, 12:09 PM   #2
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Re: CHanging the range of mod x

If you have:

then you have two cases from the definition of the modulus:

i)

ii) >-2" />

The intersection of the two cases is:



We may also choose to interpret |x| as the distance of x from the origin, which must be less than 2. So plot the two points two units from the origin as endpoints and take everything in between, but not including the endpoints since the inequality is strict.
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