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)
The person who is correct is person
___

Answer 1

To determine which person is correct regarding the values being solutions to the compound inequality \(-2 \leq 2x - 2 < 8\), we can first solve the inequality.

Step 1: Break down the compound inequality

The compound inequality consists of two parts:

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

Step 2: Solve the first part

For \(-2 \leq 2x - 2\):

Add 2 to both sides: \[ -2 + 2 \leq 2x \] \[ 0 \leq 2x \] Divide by 2: \[ 0 \leq x \]

This means \(x \geq 0\).

Step 3: Solve the second part

For \(2x - 2 < 8\):

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

Step 4: Combine the results

So, the solution for the compound inequality \(-2 \leq 2x - 2 < 8\) is: \[ 0 \leq x < 5 \]

Step 5: Check the proposed solutions

• Sophie says that \(-2\) is a solution. Since \(-2 < 0\), Sophie is not correct.
• Adola says that \(5\) is a solution. Since \(5\) is not less than \(5\) (it is equal), Adola is not correct.
• Gilly says that \(2\) is a solution. Since \(2\) is between \(0\) and \(5\) (inclusive of \(0\) and exclusive of \(5\)), Gilly is correct.

Conclusion

The correct person is person 3 (Gilly).