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.

Question

The person who is correct is?

Answer 1

To solve the compound inequality −2≤2x−2<8, we can start by isolating the x term.

Adding 2 to all parts of the compound inequality, we get:
-2 + 2 ≤ 2x − 2 + 2 < 8 + 2
0 ≤ 2x < 10

Then, dividing all parts of the compound inequality by 2, we have:
0/2 ≤ 2x/2 < 10/2
0 ≤ x < 5

So, the solution set for the compound inequality is 0 ≤ x < 5.

Checking the values given by Sophie, Adola, and Gilly:
- Sophie claimed −2 is a solution, but -2 is not in the solution set of 0 ≤ x < 5.
- Adola claimed 5 is a solution, but 5 is not in the solution set of 0 ≤ x < 5.
- Gilly claimed 2 is a solution, and 2 is indeed in the solution set of 0 ≤ x < 5.

Therefore, Gilly is correct. The person who is correct is 3 for Gilly.