Question

N is an integer such that 3n + 4 < 19 and

10n/n+ 16 > 1
Find all the possible values of n.

Answer 1

n = 3,4,5

Explanation:

3n + 4 < 19

3n ≤ 15

n ≤ 5

10n/n+16 > 1

10n > n²+16

-n²+10n-16

(-n+2)(n-8)

n = 2 or n = 8

2 < n < 8

So 2<n≤5 = 3,4,5

Answer 2

Explanation:

3n+4<19

3n<19-4

3n<15

n<5

`(10n)/(n+16 ) >1\\either~ both~ the~ denominator ~ and ~ numerator ~are ~positive ~ or ~both ~are ~ negative.\\let~ 10 n>0 \\n+16 >0\\n>-16\\again ~10 n>n+16\\9n>16\\n>(16)/(9) ~...(1)\\and ~\\10n<0,n<0\\and ~n+16 <0\\n<-16\\again\\10n<n+16\\9n<16\\n<(16)/(9) \\combining\\n<-16`

combining

(-∞,-16)U(16/9,5)