Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8

Question

. 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)

Answer 1

To solve the compound inequality \(-2 \leq 2x - 2 < 8\), let's analyze it step by step.

1. First part: Solve \(-2 \leq 2x - 2\)

   Add 2 to both sides: \[ 0 \leq 2x \] Divide both sides by 2: \[ 0 \leq x \quad \text{or} \quad x \geq 0 \]

2. Second part: Solve \(2x - 2 < 8\)

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

Now we combine the results from both parts: \[ 0 \leq x < 5 \]

This means the solution set for \(x\) is: \[ x \in [0, 5) \]

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

• Sophie says that \(-2\) is a solution. \(-2\) is not in the interval \([0, 5)\) (FALSE).

• Adola says that \(5\) is a solution. \(5\) is not in the interval \([0, 5)\) (FALSE).

• Gilly says that \(2\) is a solution. \(2\) is in the interval \([0, 5)\) (TRUE).

Thus, Gilly is the one who is correct.

The answer is 3.