Select the assumption necessary to start an indirect proof of the statement. if 3a+7 < 28, then a< 7.

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.

assume a≥7

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