Question 807894
Let x be an integer


So 2x is always even


Forcing 2x + 1 to always be odd


The next odd number after that is (2x+1)+2 = 2x + 3


The next odd number after that is (2x+3)+2 = 2x + 5


The next odd number after that is (2x+5)+2 = 2x + 7



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Add up the four integers. Then set this sum equal to 128


(2x+1)+(2x+3)+(2x+5)+(2x+7) = 128


2x+1+2x+3+2x+5+2x+7 = 128


8x+16 = 128


8x = 128-16


8x = 112


x = 112/8


x = 14


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Since x = 14, we know 


2x+1 = 2*14 + 1 = 29


2x+3 = 2*14 + 3 = 31


2x+5 = 2*14 + 5 = 33


2x+7 = 2*14 + 7 = 35



So the four consecutive odd integers are: 29, 31, 33, 35


The smallest number is <font color="red">29</font>