Solve the absolute value inequality 2|x+4|≥14. Provide the solution using interval notation.(1 point)%0D%0AThe solution is

Answer 1

To solve the inequality \( 2|x+4| \geq 14 \), we first divide both sides by 2:

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

This absolute value inequality means that either:

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

Now we will solve each case separately:

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:

\[ x \leq -11 \]

Now we combine the two parts of the solution. The solution set can be written in interval notation as:

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

Thus, the solution to the absolute value inequality \( 2|x+4| \geq 14 \) is:

\[ \boxed{(-\infty, -11] \cup [3, \infty)} \]