How many different integers, n, are there such that the difference between 2 x n squared and 7 is less than 1?

Question

The supposed answer is 6 but i have NO idea how that's possible??

Answer 1

|2n^2 - 7| < 1

We could go into a formal solution with all the AND and OR operators, but clearly n must be a small integer, so lets just try some values of n

n = 0 ---> |-7| < 1 , no
n = ± 1 --> |2-7| < 1 , no
n = ± 2 ---> |8-7| < 1 , no
n = ± 3 ---> | 18-7| < 1 no

for larger ± n's the situation is getting even worse

I don't see a single integer that would work

by definition |anything| ≥ 0
so
0 < 2n^2 - 7 < 1
7 < 2n^2 < 8

no integer value of n fits that statement.

Answer 2

The question you were looking for, well, nine years ago...
It is n squared root not n squared for which the answer is 6
You copied the question wrong.