Question

|y+4|<4 Absolute Value

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the inequality |y + 4| < 4, we can break it down into two separate inequalities based on the two cases when the expression inside the absolute value is either positive or negative.

Case 1: y + 4 > 0
In this case, the absolute value function can be simplified without the absolute value:
y + 4 < 4
Subtracting 4 from both sides: y < 0

Case 2: y + 4 < 0
In this case, the absolute value function can be simplified by multiplying both sides by -1 and changing the direction of the inequality:
-(y + 4) < 4
Simplifying: -y - 4 < 4
Adding y to both sides: -4 < y + 4
Subtracting 4 from both sides: -8 < y

Combining both cases, we have the solution:
-8 < y < 0