Answer to Question #8213 in Real Analysis for abhi

Question

x belongs to r which satisfy the inequality |x|+|x+1|<2 find all x

Answer 1

|x|+|x+1|<2
first we need to find zeroes of modules. It's x=0, x=-1Then we divide coordinate line into several segments where expressions under
modules save sign and solve inequalities in each zone.
So we have: 1. x<=-1
-x+(-x-1)<2
-2x<3
x>-3/2
so we have -3/2<x<=-1

2. -1<x<=0
-x+x+1<2
1<2
so -1<x<=0

3. x>0
x+x+1<2
2x<1
x<1/2
se we have 0<x<1/2

Finally we obtain -3/2<x<1/2 - answer