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The solution set of the equation mod(2 x -1)+mod(4-2 x )≤3 is,

The solution set of the equation


mod(2x-1)+mod(4-2x)≤3  is,

Grade:12

1 Answers

bibhash jha
15 Points
12 years ago

For x<=0,


1-2^x +4-2^x<=3

2<=2^(x+1)

x+1>=1

x>=0   .. so x=0 belongs to solution.


0<x<=2

2^x-1+4-2^x>=3

3>=3 -------- always true so [0,2]  is a solution now


x>2


2^x-1+2^x-4<=3

2^(x+1)<=8=2^3

x+1<=3

x<=2 ---------no solution in this case


so the final solution is x [0,2]

 

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