Question 277460
Given 
n is a non-zero integer and
{{{2-(16/n) < 6}}}
find n
{{{2-(16/n) < 6}}} collect like terms
{{{-(16/n) < 4}}}
{{{-4/n < 0 }}}
Now here is the tricky part. In order to isolate n, we need to multiply through by n. If n is positive, then the inequality sign stays 'less than'. However, if n is negative, then the inequalty changes to 'greater than'.

{{{-4 < n}}} when n > 0
{{{-4 > n }}} when n < 0

Every one of the possible answers A through E are negative. So we need to use the second equation.

{{{-4 > n }}}
Which possible answers are less than -4? Only -8 and -6 (A and B)

BUT, your problem stated the result had to be < 6 and an integer. You can see that 16/-6 is not an integer, so -6 won't work. 16/-8 is an integer. 

Answer is -8 (A)

Check that answer by plugging -8 in
{{{2 - (16/(-8)) < 6}}}
{{{2 + 2 < 6}}} 
{{{4 < 6}}} which is true. So -8 works