What are the problems? Can you type them here, not everyone has that book.
I'm a high school sophomore using the Spivaks calc book. The beginning of this book is mostly about proving basic things etc. We can only use what we have proven and all that. I get it for the most part but I am totally stuck on 9 and 10. Please help? I am stressing out so much. I don't even know how to start on these.
Express each of the following without absolute value signs, treating each case separately when necessary.
|a+b| - |b|
My problem is I don't know how to get started, because I don't know if my starting point is right. It says treating each case separately when necessary, and I don't know if it is necessary but I'll try.
If a and b are both positive, |a+b| is a+b and |b| is b. So it would be a + b - b which would be a.
If a and b are both negative, |a+b| is also a+b and |b| is also b. So it would be a+b - b, this would also be a.
If a is positive and b is negative, |a+b| would be |a-b| and |b| would be b. Here's where I start to get a bit confused. I don't know how to show |a-b| without absolute values the correct way. Sorry if that's a really lame question but I'm kinda bad at this. am I even approaching that the right way??
The next question is:
|(|x| - 1)| and again I don't know if I am approaching this the right way. If x is positive, it'd be |x - 1|, I think? But how would I write that? What if x is more than 1 but less than 0? then x - 1 would be a negative number, and from an absolute value, how would that work?