Question

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 who is correct, we need to solve the compound inequality \( -2 \leq 2x - 2 < 8 \).

Let's break it down into two parts:

1. Solve the left part of the compound inequality:
\[
-2 \leq 2x - 2
\]
Adding 2 to both sides gives:
\[
0 \leq 2x
\]
Dividing by 2:
\[
0 \leq x \quad \text{or} \quad x \geq 0
\]

2. Solve the right part of the compound inequality:
\[
2x - 2 < 8
\]
Adding 2 to both sides gives:
\[
2x < 10
\]
Dividing by 2:
\[
x < 5
\]

Now we combine the results of both parts:
\[
0 \leq x < 5
\]
This means the solution set is \( x \) such that \( x \) is between 0 and 5, including 0 but excluding 5.

Now we check the values proposed by Sophie, Adola, and Gilly:
- Sophie claims \( -2 \) is a solution: **Not correct** because \( -2 < 0 \).
- Adola claims \( 5 \) is a solution: **Not correct** because \( 5 \) is not included (it is excluded).
- Gilly claims \( 2 \) is a solution: **Correct** because \( 2 \) is between 0 and 5.

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