Question

N is an integer such that
3n+4 <19 and 10n/n^2+16Find all the possible values of n

Answer 1

3n+4<19

3n<19-4

3n<15

n<15/3

n<5-------(1)

4n²=16

(2n)²=4²

2n=4

n=2-------(2)

so, n=2 or n<5

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hope it helps

Answer 2

n = {3 , 4 , 5} if n is an integer such that 3n+4 ≤ 19 and 10n/(n² + 16) > 1  

n = {3 , 4  } if n is an integer such that 3n+4 < 19 and 10n/(n² + 16) > 1  

Step 1:

Solve 3n+4 ≤19

Subtract 4 from both sides

3n ≤ 15

Divide by 3 both sides

n ≤ 5

if  3n+4  < 19 considered the n < 5

Step 2:

Solve  10n/(n² + 16) > 1  

as n² + 16 is +ve

Hence

n² + 16 < 10 n

=>  n² - 10n + 16 < 0

=> (n - 8)(n - 2) < 0

=>  2 < n < 8

Step 3:

Combine both results

n ≤ 5  and 2 < n < 8

Hence  2 < n ≤ 5

n is an integer so n = {3 , 4 , 5}

if  3n+4  < 19 considered the n < 5  hence 2 < n < 5 r so n = {3 , 4 }

Complete and Correct Question.

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