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

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ANSWER

$n < - 3 \: or \: n> - 2$

EXPLANATION

The given inequality is,

$|2n + 5| \: > \: 1$

By the definition of absolute value,

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

We divide through by negative 1, in the first part of the inequality and reverse the sign to get,

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

We simplify now to get,

$2n \: < \: - 1 - 5 \: or \: 2n \: > \: 1 - 5$

$2n \: < \: - 6 \: or \: 2n \: > \: - 4$

Divide through by 2 to obtain,

$n \: < \: - 3 \: or \: n \: > \: - 2$

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