Question

Solve the compound inequality.
negative 2 less than 2 x minus 2 less than or equals 8
Question content area bottom
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is
  
enter your response here. ​(Type your answer in interval​ notation.)
B.
The solution set is the empty set.

Answer 1

To solve the compound inequality \(-2 < 2x - 2 \leq 8\), we will break it down into two parts.

1. Solve the left inequality:

\[
-2 < 2x - 2
\]

Add 2 to both sides:

\[
0 < 2x
\]

Now, divide by 2:

\[
0 < x \quad \text{or} \quad x > 0
\]

2. Solve the right inequality:

\[
2x - 2 \leq 8
\]

Add 2 to both sides:

\[
2x \leq 10
\]

Now, divide by 2:

\[
x \leq 5
\]

Combining both parts, we have:

\[
0 < x \leq 5
\]

In interval notation, this is represented as:

\[
(0, 5]
\]

So, the correct choice is:

**A. The solution set is \((0, 5]\)**.