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
.
Remaining Attempts : 3

Answer 1

Let's solve the compound inequality \(-2 \leq 2x - 2 < 8\).

We can break this down into two separate inequalities:

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

Starting with the first inequality:

\(-2 \leq 2x - 2\)

Add 2 to both sides:

\[ 0 \leq 2x \]

Divide both sides by 2:

\[ 0 \leq x \quad \text{or} \quad x \geq 0 \]

Now, for the second inequality:

\(2x - 2 < 8\)

Add 2 to both sides:

\[ 2x < 10 \]

Divide both sides by 2:

\[ x < 5 \]

Combining both results, we have:

\[ 0 \leq x < 5 \]

This means that \(x\) can take any value from 0 up to (but not including) 5.

Now let's check each person's claim:

1. Sophie claims \(x = -2\):

   • \(-2\) is not in the interval \([0, 5)\), so Sophie is incorrect.

2. Adola claims \(x = 5\):

   • \(5\) is not in \([0, 5)\) (it is excluded), so Adola is incorrect.

3. Gilly claims \(x = 2\):

   • \(2\) is in the interval \([0, 5)\), so Gilly is correct.

Thus, the person who is correct is person 3 (Gilly).