Question

How many integers n leave remainder 4 when divided by 7, if n satisfies the given inequality?

Answer 1

Consider inequality $|-n|$ This inequality is equivalent to inequality $|n|$

This means that $-46$

The greatest integer number n, such that $-46$ 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.