Question

Daca a∈ℕ demonstrati, folosind proprietatile relatiei de inegalitate, ca :
a) 2a+1 < 3a+2
b) 4a+5 ≤ 5a+5
c) a-4 < 2a-2
d) 3(a+1) < 4(a+2)

Answer 1

2a + 1 < 3a + 2
2a - 3a < 2 - 1
- a < 1
a > - 1
a = ( 0 , 1 , 2, 3 .....)

4a + 5 ≤5a + 5
4a - 5a  ≤ 5 - 5
- a ≤ 0
a ≥ 0
a = ( 0 , 1 , 2, 3, ......)

a - 4 < 2a - 2
a - 2a < 4 - 2
- a < 2
a > - 2
a = ( 0 , 1, 2, ......)

3 ( a+ 1 )< 4 (a + 2 )
3a + 3 < 4a + 8
3a - 4a < 8 - 3
- a < 5
a > - 5
a = ( 0 ,1,2,3......)