Algebra-1

To solve the inequality -5 |4 + n| < -15, we can begin by dividing both sides of the inequality by -5. However, we need to be careful about the direction of the inequality when dividing by a negative number. Dividing both sides by -5 reverses the inequality sign, which gives us:

|4 + n| > 3

Now, we can break it down into two cases:

Case 1: 4 + n is nonnegative (i.e., 4 + n ≥ 0)
In this case, the absolute value |4 + n| is equal to 4 + n, so we have:
4 + n > 3

Solving this inequality, we get:
n > 3 - 4
n > -1

Case 2: 4 + n is negative (i.e., 4 + n < 0)
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