Solve Inequality Problem Step by Step

[betosasana]

How can I solve, step by step, this inequality ?
The result I have is [ 1 , (-1 + sqrt33)/2 ]
but the result should be [ 0 , (-1 + sqrt33)/2 ]|x+2|-|x-1|$$\geq$$$$\sqrt{x^2+x+1}$$


thanks for ur help =)

 

[danago]

How did you go about solving it? Its a little hard to point out where you went wrong without actually seeing what you did. If i was doing it, i'd solve the inequality separately over three different intervals of x and then conglomerate my three solutions into a final answer.

 

[betosasana]

How did you go about solving it? Its a little hard to point out where you went wrong without actually seeing what you did. If i was doing it, i'd solve the inequality separately over three different intervals of x and then conglomerate my three solutions into a final answer.

Please, would you do it and let me know if you got the answer given ?
Coz I took the 3 intervals, but I do not know how to use the restriction |x+2|-|x-1|>=0 on the final results.

 

[danago]

I just did it and got $x \in [ 0 , \frac{-1+\sqrt{33}}{2} ]$.

If i had to make a guess, i would say that you have solved the inequality incorrectly for the case where -2<x<1

 

[betosasana]

I just did it and got $x \in [ 0 , \frac{-1+\sqrt{33}}{2} ]$.

If i had to make a guess, i would say that you have solved the inequality incorrectly for the case where -2<x<1

And would it be too much if I ask you to explain it step by step ?
Pleeeeaaaase =P

 

[danago]

How about you show me how you did it and ill point out what went wrong? You were very close to the correct answer, after all.