Describe and diagram the set determined by the condition

mxc
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Homework Statement


0<\left|x+3\right|<1/4


Homework Equations





The Attempt at a Solution


(-13/4)<x<(-11/4) and x\neq-3

Thanks in advance. This is my first post and I am unfamiliar with formatting this kind of stuff so I will work on getting better at that aspect.
 
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mxc said:

Homework Statement


0<\left|x+3\right|<1/4


Homework Equations





The Attempt at a Solution


(-13/4)<x<(-11/4) and x\neq-3

Thanks in advance. This is my first post and I am unfamiliar with formatting this kind of stuff so I will work on getting better at that aspect.

That looks OK. What's your question?
 
The book says the solution is (-13/4)<x<(-11/4).

It should be noted that this particular book is notorious for being rife with errors, but I always want to make sure that I am not wrong. Thank you LCKurtz.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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