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