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What is the soln of 2x+2|x|>2(2)1/2

8 years ago

147 Points

Dear chilukuri

case 1 x>=0

2x+2|x|>2(2)1/2

2x+2x>2(2)1/2

2x>(2)1/2

x>=1/2

case 2   x<0

2x+2|x|>2(2)1/2

or 2x+2-x>2(2)1/2

or 22x+1>22x(2)1/2

simplify

(2x -21/2 -1)((2x -21/2 +1)>0

first bracket is always negative so second bracket should also be negative

(2x -21/2 +1)<=0

2x <=21/2 -1

xln2 <=ln(21/2 -1)

x<=ln2(21/2 -1)

so final solution

x<=ln2(21/2 -1)         and x>=1/2

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Regards,

8 years ago
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