Solve the absolute value inequality 2|x+4|≥14 . Provide the solution using interval notation.(1 point)

Question

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Answer 1

To solve the absolute value inequality \( 2|x + 4| \geq 14 \), we can start by isolating the absolute value:

\[ |x + 4| \geq 7 \]

This inequality can be split into two separate cases:

1. \( x + 4 \geq 7 \)
2. \( x + 4 \leq -7 \)

Case 1: \( x + 4 \geq 7 \)

Subtracting 4 from both sides gives:

\[ x \geq 3 \]

Case 2: \( x + 4 \leq -7 \)

Subtracting 4 from both sides gives:

\[ x \leq -11 \]

Combining the Solutions

The solutions from the two cases are:

1. \( x \geq 3 \)
2. \( x \leq -11 \)

Therefore, the solution in interval notation is:

\[ (-\infty, -11] \cup [3, \infty) \]

So, the final answer is:

\[ (-\infty, -11] \cup [3, \infty) \]