Question

Solving Inqualities.

|x| - |x-1| < 1

Answer 1

need cases for this one

Answer 2

if \(x>1\) then \(|x-1|=x-1\) and \(|x|=x\) so you get
\[x-(x-1)<1\]\[1<1\] which is false, so it is never true when \(x>1\)

Answer 3

if \(x<0\) then \(|x|=-x\) and \(|x-1|=1-x\) so you get
\[-x-(1-x)<1\]
\[-1<1\] and so it is always true of \(x<0\)

Answer 4

last job is to figure out what happens is \(0<x<1\)

Answer 5

I get that as the solution too. 0< x < 1.

However it seems the solution should be -infinity < x < 1.