n is an integer such that 3n + 2 ≤ 14, and 6n/(n^2 + 5) >1. Find all possible values of n.
Step 1: Simplify 3n + 2 ≤ 14 3n ≤ 12 n ≤ 4 and 6n > n^2 + 5 0 > n^2 -6n + 5 Factorise (n-5)(n-1) < 0
Step 2: Let (n-5)(n-1) = 0, so n=5 or n=1 If (n-5)(n-1) < 0, then 1<n<5 (use graph/substitution)
Step 3: Combine, n can take values 2,3,4.
CM
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