When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.
In our case we assume a is not smaller than 7, that is we assume a≥7.
a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:
3a+7≥28,
which is a contradiction because 3a+7 is smaller than 28.
So our assumption is wrong, which means the opposite of it is correct.
Answer: assume a≥7