ANSWER
[tex]n < - 3 \: or \: n> - 2[/tex]
EXPLANATION
The given inequality is,
[tex] |2n + 5| \: > \: 1[/tex]
By the definition of absolute value,
[tex] - (2n + 5) \: > \: 1 \: or \: (2n + 5) \: > \: 1[/tex]
We divide through by negative 1, in the first part of the inequality and reverse the sign to get,
[tex] 2n + 5 \: < \: - 1 \: or \: (2n + 5) \: > \: 1[/tex]
We simplify now to get,
[tex] 2n \: < \: - 1 - 5 \: or \: 2n \: > \: 1 - 5[/tex]
[tex] 2n \: < \: - 6 \: or \: 2n \: > \: - 4[/tex]
Divide through by 2 to obtain,
[tex] n \: < \: - 3 \: or \: n \: > \: - 2[/tex]
