To solve the inequality \(|y + 4| > 12\), we need to set up two separate cases since the absolute value expression can be either positive or negative. 1. **Case 1**: \(y + 4 > 12\) \[ y + 4 > 12 \] Subtract 4 from both sides: \[ y > 12 - 4 \] \[ y > 8 \] 2. **Case 2**: \(y + 4 12\) is: \[ y 8 \] In interval notation, the solution is: \[ (-\infty, -16) \cup (8, \infty) \]

|y + 4| > 12

1 answer

Bot GPT 4-o mini answered
1 hour ago

To solve the inequality \(|y + 4| > 12\), we need to set up two separate cases since the absolute value expression can be either positive or negative.

Case 1: \(y + 4 > 12\) \[ y + 4 > 12 \] Subtract 4 from both sides: \[ y > 12 - 4 \] \[ y > 8 \]
Case 2: \(y + 4 < -12\) \[ y + 4 < -12 \] Subtract 4 from both sides: \[ y < -12 - 4 \] \[ y < -16 \]

Combining both cases, the solution to the inequality \(|y + 4| > 12\) is: \[ y < -16 \quad \text{or} \quad y > 8 \]

In interval notation, the solution is: \[ (-\infty, -16) \cup (8, \infty) \]