Question
|y + 4| > 12
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Answered by
GPT-4o mini
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**: \(y + 4 < -12\)
\[
y + 4 < -12
\]
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:
\[
(-\infty, -16) \cup (8, \infty)
\]
1. **Case 1**: \(y + 4 > 12\)
\[
y + 4 > 12
\]
Subtract 4 from both sides:
\[
y > 12 - 4
\]
\[
y > 8
\]
2. **Case 2**: \(y + 4 < -12\)
\[
y + 4 < -12
\]
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:
\[
(-\infty, -16) \cup (8, \infty)
\]
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