Consider inequality [tex]|-n|<46.[/tex] This inequality is equivalent to inequality [tex]|n|<46.[/tex]
This means that [tex]-46<n<46.[/tex]
The greatest integer number n, such that [tex]-46<n<46[/tex] when dividing by 7 gives the remainder 4 is 39. Then subtract 7, you get 32, then 25 and so on.
When n=-39, -32, -25, -18, -11, -4, 4, 11, 18, 25, 32, 39 then dividing by 7 the remainder is 4.
Answer: 12 integers.
