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Solute in 2^|x+1|- |2^x-1|=2^x +1?

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uoor | Student, College Freshman | eNoter

Posted January 3, 2012 at 11:25 PM via web

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Solute in 2^|x+1|- |2^x-1|=2^x +1?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 3, 2012 at 11:53 PM (Answer #1)

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You need to discuss three cases such that:

I) If x<-1 => `2^(-x-1) + 2^x - 1 = 2^x + 1`

Reducing like powers yields:

`1/2^(x+1) = 2 =gt 1/(2*2^x) =2 =gt 1/2^x = 2^2 =gt 2^x = 1/2^2 =gt 2^x = 2^(-2)`

Equating the exponents yields: x = -2

II) If x in [-1 ; 0] => the unique solution to the equation is x = 0

III) If x>0 => The solution to the equation may be any positive value.

Hence, considering all three cases, the solutions to the equation are: `{-2}U[0,oo).`

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