Question

Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8
. Sophie says that −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 which person's claim is correct regarding the compound inequality \(-2 \leq 2x - 2 < 8\), we need to solve the inequality.

1. Split the compound inequality into two parts:
\[
-2 \leq 2x - 2 \quad \text{and} \quad 2x - 2 < 8
\]

2. Solve the first part:
\[
-2 \leq 2x - 2
\]
Add 2 to both sides:
\[
0 \leq 2x
\]
Divide by 2:
\[
0 \leq x \quad \text{or} \quad x \geq 0
\]

3. Solve the second part:
\[
2x - 2 < 8
\]
Add 2 to both sides:
\[
2x < 10
\]
Divide by 2:
\[
x < 5
\]

4. Combining both parts, we have:
\[
0 \leq x < 5
\]
This means the solution set is all \(x\) such that \(x\) is between 0 and 5, inclusive of 0 but exclusive of 5.

Now, let's evaluate the claims:
- Sophie claims that \(-2\) is a solution. This is incorrect since \(-2\) is not in the range \(0 \leq x < 5\).
- Adola claims that \(5\) is a solution. This is also incorrect since \(5\) is not included in the range.
- Gilly claims that \(2\) is a solution. This is correct since \(2\) is within the range \(0 \leq x < 5\).

Thus, the person who is correct is person **3** (Gilly).