Question

Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8
−
2
≤
2
𝑥
−
2
<
8
. Sophie says that −2
−
2
is a solution. Adola says that 5 is a solution. Gilly says that 2 is a solution. Which person is correct? Enter 1 for Sophie, 2 for Adola, or 3 for Gilly.(1 point)
The person who is correct is person .

Answer 1

To determine who is correct, we need to solve the compound inequality:

\[
-2 \leq 2x - 2 < 8
\]

We can break this down into two parts.

**Part 1: Solve \(-2 \leq 2x - 2\)**

1. Add 2 to both sides:
\[
0 \leq 2x
\]
2. Divide by 2:
\[
0 \leq x
\]
or
\[
x \geq 0
\]

**Part 2: Solve \(2x - 2 < 8\)**

1. Add 2 to both sides:
\[
2x < 10
\]
2. Divide by 2:
\[
x < 5
\]

Combining the results from both parts, we have:
\[
0 \leq x < 5
\]

Now let's check the claims made by Sophie, Adola, and Gilly:

- **Sophie says that \(-2\) is a solution.**
\( -2 \) does not satisfy \( 0 \leq x < 5\). (Incorrect)

- **Adola says that \(5\) is a solution.**
\(5\) does not satisfy \(0 \leq x < 5\). (Incorrect)

- **Gilly says that \(2\) is a solution.**
\(2\) satisfies \(0 \leq 2 < 5\). (Correct)

Thus, the person who is correct is person **3**.