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.
The person who is correct is?
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.
To determine who is correct, we need to solve the compound inequality −2 ≤ 2x - 2 < 8 step-by-step.
First, let's solve for the lower bound:
-2 ≤ 2x - 2
Adding 2 to both sides:
0 ≤ 2x
Dividing both sides by 2:
0 ≤ x
Now let's solve for the upper bound:
2x - 2 < 8
Adding 2 to both sides:
2x < 10
Dividing both sides by 2:
x < 5
So, the solution set for the compound inequality is 0 ≤ x < 5.
We can now determine who is correct:
- Sophie says that -2 is a solution. Let's check: -2 is not within the solution set.
- Adola says that 5 is a solution. Let's check: 5 is not within the solution set.
- Gilly says that 2 is a solution. Let's check: 2 is within the solution set.
Therefore, the person who is correct is Gilly (person 3).