It is not necessary to state that the lesser number is positive, since
if it were negative, both the lesser and greater would be negative, and
you cannot increase a negative with a negative.  And 0 is out because
twice zero is zero, and there could be no lesser and greater.

x = lesser (positive) integer
2x = greater integer

2x + 2x ≥ 45
     4x ≥ 45
      x ≥ 11.25

Since x is an integer, x=12.  

Edwin