Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality -2<2x-2<8.

Answer 1

To solve the compound inequality \(-2 < 2x - 2 < 8\), we can break it down into two parts and solve each part separately.

1. Solve the left part of the inequality: \[ -2 < 2x - 2 \] Add 2 to both sides: \[ 0 < 2x \] Divide by 2: \[ 0 < x \quad \text{or} \quad x > 0 \]

2. Solve the right part of the inequality: \[ 2x - 2 < 8 \] Add 2 to both sides: \[ 2x < 10 \] Divide by 2: \[ x < 5 \]

Now, we can combine the two results: \[ 0 < x < 5 \]

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

This means that the potential values for \(x\) lie in the interval greater than 0 and less than 5.