SOLUTION: Please answer the foloowing question: |x^2+2|x|+3|>4

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Question 200576: Please answer the foloowing question:

|x^2+2|x|+3|>4
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Given equation: abs%28x%5E2+%2B+2abs%28x%29+%2B+3%29+%3E+4

Case 1: x > 0
abs%28x%5E2+%2B+2x+%2B+3%29+%3E+4
abs%28%28x%2B1%29%5E2+%2B+2%29+%3E+4
%28x%2B1%29%5E2+%2B+2+%3E+4
%28x%2B1%29%5E2+%2B+2+-+4+%3E+4+-+4
%28x%2B1%29%5E2+-+2+%3E+0
%28x%2B1%29%5E2+-+%28sqrt%282%29%29%5E2+%3E+0
%28%28x%2B1%29+%2B+sqrt%282%29%29%2A%28%28x%2B1%29+-+sqrt%282%29%29+%3E+0
%28x%2B1%2Bsqrt%282%29%29%2A%28x%2B1-sqrt%282%29%29+%3E+0
x+=+sqrt%282%29+-+1 [since the other solution is not feasible as x > 0]

Case 2: x < 0
abs%28x%5E2+-+2x+%2B+3%29+%3E+4
abs%28%28x-1%29%5E2+%2B+2%29+%3E+4
%28x-1%29%5E2+%2B+2+%3E+4
%28x-1%29%5E2+%2B+2+-+4+%3E+4+-+4
%28x-1%29%5E2+-+2+%3E+0
%28x-1%29%5E2+-+%28sqrt%282%29%29%5E2+%3E+0
%28%28x-1%29+%2B+sqrt%282%29%29%2A%28%28x-1%29+-+sqrt%282%29%29+%3E+0
%28x-1%2Bsqrt%282%29%29%2A%28x-1-sqrt%282%29%29+%3E+0
x+=+-sqrt%282%29+%2B+1 [since the other solution is not feasible as x < 0]