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 GillyThe person who is correct is person

Answer 1

To determine which person's claim about the solution set of the compound inequality \(-2 \leq 2x - 2 < 8\) is correct, we first need to solve the compound 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. Combine the results: \[ 0 \leq x < 5. \]

Now, we evaluate the claims made by Sophie, Adola, and Gilly:

• Sophie claims that \(-2\) is a solution. (False, since \(-2 < 0\))
• Adola claims that \(5\) is a solution. (False, since \(5 \not< 5\))
• Gilly claims that \(2\) is a solution. (True, since \(2\) is between \(0\) and \(5\))

The correct answer is Gilly.

So, the person who is correct is person 3.