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).