Question

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:

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