Prove using proof by contradiction: if x is an even integer, then 3x + 7 is odd

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asked Aug 20, 2019 187k views

1 Answer

J Richard Snape · Answer 1 · 2019-08-26T06:14:19+0000

Suppose 3x + 7 is even when x is even

then 3x + 7 = 2m where m is some integer

3x = 2m - 7

which means that 3x is odd because 2m - 7 must be odd
but x is even and 3x is even so our original assumption is wrong

So 3x - 7 must be odd when x is even.

Prove using proof by contradiction: if x is an even integer, then 3x + 7 is odd

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