I'm doing some induction problems but i'm getting stuck when I have inequations and not equations.
For example:

3^n = 2^(n+1) + 1 ,for n Natural \{1}

p(2) = 9 = 9

Hypotheses: 3^n = 2^(n+1) + 1

Thesis: (I don't get part of it so if you could explain the all process I would be glad)

3^(n+1) = 3^n * 3 = 3( 2^(n+1) +1) =
2^(n+1) * 3 + 3 = 2^(n+1)*3 + 1 = 2^(n+2) +1

Thanks

Question

I'm doing some induction problems but i'm getting stuck when I have inequations and not equations. 
For example: 

3^n >= 2^(n+1) + 1 ,for n Natural \{1}

p(2) = 9 >= 9

Hypotheses: 3^n >= 2^(n+1) + 1

Thesis: (I don't get part of it so if you could explain the all process I would be glad)

3^(n+1) = 3^n * 3 >= 3( 2^(n+1) +1) =
2^(n+1) * 3 + 3 >= 2^(n+1)*3 + 1 = 2^(n+2) +1

Thanks