Question

Solve the absolute value inequality
2
|
x
+
11
|
+
17
>
3
. Provide the answer using interval notation.(1 point)


The solution to
2
|
x
+
11
|
+
17
>
3
is (
)

Answer 1

To solve the absolute value inequality \( 2|x + 11| + 17 > 3 \), we will first isolate the absolute value expression.

1. Subtract 17 from both sides:

\[
2|x + 11| > 3 - 17
\]

\[
2|x + 11| > -14
\]

2. Divide both sides by 2:

\[
|x + 11| > -7
\]

Since the absolute value expression \( |x + 11| \) is always non-negative (greater than or equal to 0), the inequality \( |x + 11| > -7 \) holds for all real numbers \( x \). Thus, the solution includes all real numbers.

**In interval notation, the solution is**:

\[
(-\infty, \infty)
\]