Question

sophie, adola, and gilly are debating potential values in the solution set of the compound inequality $-2 \leq 2x - 2 < 8$. 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 $\square$.

Explanation:

Step1: Solve the compound inequality

First, solve the compound inequality \(-2 \leq 2x - 2 < 8\).

Add 2 to all parts of the inequality:

\(-2 + 2 \leq 2x - 2 + 2 < 8 + 2\)

Simplify each part:

\(0 \leq 2x < 10\)

Then divide all parts by 2:

\(\frac{0}{2} \leq \frac{2x}{2} < \frac{10}{2}\)

Which gives:

\(0 \leq x < 5\)

Step2: Check each person's value

• Sophie says \(x = -2\). But \(-2\) is less than \(0\), so it is not in the solution set \(0 \leq x < 5\).
• Adola says \(x = 5\). But the inequality is \(x < 5\) (not less than or equal to), so \(5\) is not in the solution set.
• Gilly says \(x = 2\). Since \(0 \leq 2 < 5\), \(2\) is in the solution set.

Answer:

3