Question 923732
No positive integer n satisfies 11n + 17 <= 2n (this is equivalent to n <= -17/9).


Proof: n = 1 --> 11*1 + 17 <= 2*1, which is not true. Suppose that some k >= 1 does not satisfy inequality, which occurs iff 11k + 17 > 2k. We wish to show that k+1 also does not satisfy the inequality, i.e. we wish to show


*[tex \large 11(k+1) + 17 > 2(k+1)]
*[tex \large 11k + 17 + 11 > 2k + 2]


However by hypothesis, 11k+17 > 2k, so *[tex \large 11k + 17 + 11 > 2k + 11 > 2k + 2], which is a true statement, so k+1 also does not satisfy 11n + 17 <= 2n.