Question #20558

|2x-1|-|x+3|≥1

Expert's answer

For x>=0.5 |2x-1|=2x-1 and |x+3|=x+3

So, 2x-1-x-3>=1 x-4>=1, x>=5, so x>=5 issolution in this case

For -3<x<0.5 |2x-1|=1-2x and |x+3|=x+3

So, 2x-1+x+3>=1 3x>=-1, x>=-1/3, so,-1/3=<x<0.5 is solution in this case

For x<-3 |2x-1|=1-2x and |x+3|=-x-3

So, 1-2x+x+3>=1 -x+4>=1, so x<=3, so solution inthis case is x<-3

Summarizing we get:

x is solution in next cases: (-infinity,-3)U(-1/3,Infinity)

So, 2x-1-x-3>=1 x-4>=1, x>=5, so x>=5 issolution in this case

For -3<x<0.5 |2x-1|=1-2x and |x+3|=x+3

So, 2x-1+x+3>=1 3x>=-1, x>=-1/3, so,-1/3=<x<0.5 is solution in this case

For x<-3 |2x-1|=1-2x and |x+3|=-x-3

So, 1-2x+x+3>=1 -x+4>=1, so x<=3, so solution inthis case is x<-3

Summarizing we get:

x is solution in next cases: (-infinity,-3)U(-1/3,Infinity)

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