# Answer to Question #8213 in Real Analysis for abhi

Question #8213

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

Expert's answer

|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

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

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