What is the solution to the inequality |2n+5|>1?

Answer:ANSWERn < - 3 \: or \: n > - 2n<−3orn>−2EXPLANATIONThe given inequality is,|2n + 5| \: > \: 1∣2n+5∣>1By the definition of absolute value,- (2n + 5) \: > \: 1 \: or \: (2n + 5) \: > \: 1−(2n+5)>1or(2n+5)>1We divide through by negative 1, in the first part of the inequality and reverse the sign to get,2n + 5 \: < \: - 1 \: or \: (2n + 5) \: > \: 12n+5<−1or(2n+5)>1We simplify now to get,2n \: < \: - 1 - 5 \: or \: 2n \: > \: 1 - 52n<−1−5or2n>1−52n \: < \: - 6 \: or \: 2n \: > \: - 42n<−6or2n>−4Divide through by 2 to obtain,n \: < \: - 3 \: or \: n \: > \: - 2n<−3orn>−2