NIMCET 2009 Question Paper with solutions

© examsiri.com

Question : 25 of 120

Marks: +1, -0

If

x < -1

and

2^{|x+1|}-2 x=|2^{x}-1|+1

, then the value of

x

is

-2
2
0
1

Solution:

If

x<-1,|x+1|=-(x+1)

and

\;\; 2^{x}-1 ∣=1-2^{x}

Now,

\;\; 2^{|x-1|}-2^{x}=|2^{x}-1|+1

⇒ \;\; 2^{-(x+1)}-2^{x}=1-2^{x}+1

⇒ \;\; \;{1}/{2 ⋅ 2^{x}}-2^{x}=2-z^{x}

Let

2^{x}=y

⇒ \;\; \;{1}/{2 y}-y=2-y

⇒ \;\; \;{1}/{2 y}=2

⇒ \;\; y=\;{1}/{4}

⇒ \;\; 2^{˙{x}}=\;{1}/{4}=2^{-2}

On comparing. we get

\Rightarrow

x=-2

© examsiri.com

Go to Question:

Prev Question

Next Question