Question

Solve the absolute value inequality.
StartAbsoluteValue 2 x minus 2 EndAbsoluteValue greater than 8
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set in interval notation is
  
enter your response here.
​(Simplify your​ answer.)
B.
The solution set is empty set.
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set in interval notation is
  
enter your response here.
​(Simplify your​ answer.)
B.
The solution set is empty set.

Answer 1

To solve the absolute value inequality \( |2x - 2| > 8 \), we can break it down into two separate cases:

1. **Case 1**: \( 2x - 2 > 8 \)
2. **Case 2**: \( 2x - 2 < -8 \)

**Case 1**: Solve the inequality \( 2x - 2 > 8 \)

\[
2x - 2 > 8
\]

Add 2 to both sides:

\[
2x > 10
\]

Now, divide by 2:

\[
x > 5
\]

**Case 2**: Solve the inequality \( 2x - 2 < -8 \)

\[
2x - 2 < -8
\]

Add 2 to both sides:

\[
2x < -6
\]

Now, divide by 2:

\[
x < -3
\]

Now, we can combine the solutions from both cases. The overall solution set is:

\[
x < -3 \quad \text{or} \quad x > 5
\]

In interval notation, this is expressed as:

\[
(-\infty, -3) \cup (5, \infty)
\]

Thus, the solution set in interval notation is:

\[
\boxed{(-\infty, -3) \cup (5, \infty)}
\]