Question

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


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

Answer 1

To solve the inequality \( 2|x+11| + 17 > 3 \), we start by isolating the absolute value.

1. Subtract 17 from both sides:
\[
2|x+11| > 3 - 17
\]
This simplifies to:
\[
2|x+11| > -14
\]

Since the left side is an absolute value multiplied by 2, which is always non-negative, it is always greater than -14. Therefore, this inequality holds for all real numbers.

However, for clarity, let's simplify further:

2. Divide both sides by 2:
\[
|x+11| > -7
\]

Since the absolute value is always non-negative, it is always greater than any negative number.

Thus, the solution set is all real numbers \( x \).

In interval notation, this is expressed as:
\[
(-\infty, \infty)
\]

Therefore, the solution to the inequality \( 2|x+11| + 17 > 3 \) is \((- \infty, \infty)\).