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

We can break this compound inequality into two parts:

1. \(-2 \leq 2x - 2\)
2. \(2x - 2 < 8\)

**Solving the first part:**

\[
-2 \leq 2x - 2
\]

Adding 2 to both sides:

\[
0 \leq 2x
\]

Dividing by 2:

\[
0 \leq x \quad \text{or} \quad x \geq 0
\]

**Solving the second part:**

\[
2x - 2 < 8
\]

Adding 2 to both sides:

\[
2x < 10
\]

Dividing by 2:

\[
x < 5
\]

**Combining the results:**

From both parts, we have:

\[
0 \leq x < 5
\]

This means that \(x\) can take any value between 0 (inclusive) and 5 (exclusive).

Now, let's check the values proposed by Sophie, Adola, and Gilly:

- **Sophie says \(x = -2\)**: This is not in the solution set since \(-2 < 0\).
- **Adola says \(x = 5\)**: This is also not in the solution set since \(5\) is not less than \(5\).
- **Gilly says \(x = 2\)**: This is in the solution set since \(2\) is between \(0\) and \(5\).

Thus, only Gilly's value satisfies the compound inequality.

The person who is correct is person **3**.