Question

What is the solution to the inequality l2n+5l > 1

Answer 1

n < -3 and n > -2

Explanation:

To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 2n + 5 > 1

To solve this inequality, we have:

2n > 1 - 5

2n > -4

n > -2

Case 2: -(2n + 5) > 1

To solve this inequality, we have:

-2n - 5 > 1

-2n > 1 + 5

-2n > 6

Dividing both sides by -2 (and reversing the inequality sign):

n < -3

Combining the solutions from both cases, we have:

n < -3 or n > -2

So the solution to the inequality |2n + 5| > 1 is n < -3 or n > -2.

Answer 2

n < -3 or n > -2

Explanation:

|2n + 5| > 1

2n + 5 < -1 or 2n + 5 > 1

2n < - 6 or 2n > -4

n < -3 or n > -2