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

Mathematics

1 answer:

tekilochka [14]3 years ago

7 0

Answer:

ANSWER

n < - 3 \: or \: n > - 2n<−3orn>−2

EXPLANATION

The given inequality is,

|2n + 5| \: > \: 1∣2n+5∣>1

By the definition of absolute value,

- (2n + 5) \: > \: 1 \: or \: (2n + 5) \: > \: 1−(2n+5)>1or(2n+5)>1

We 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)>1

We simplify now to get,

2n \: < \: - 1 - 5 \: or \: 2n \: > \: 1 - 52n<−1−5or2n>1−5

2n \: < \: - 6 \: or \: 2n \: > \: - 42n<−6or2n>−4

Divide through by 2 to obtain,

n \: < \: - 3 \: or \: n \: > \: - 2n<−3orn>−2

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