Problem 2 - Entrance Test

1. Identify critical points at x = -2 (undefined denominator) and solve |x - 1| ≥ |x + 2| (after moving denominator). 2. Break into cases: x ≥ 1 → x - 1 ≥ x + 2 → -1 ≥ 2 (no solutions); 1 > x > -2 → -(x - 1) ≥ x + 2 → -x + 1 ≥ x + 2 → -1 ≥ 2x → x ≤ -0.5, but x ∈ (-2,1) → x ∈ (-2, -0.5). 3. x < -2: -(x - 1) ≤ x + 2 → -x +1 ≤ x +2 → -1 ≤ 2x → x ≥ -0.5, conflicting with x < -2 → no solution. 4. Combine intervals: (-2, -0.5]. Correct answer adjusted here, but initial options may conflict unless rephrased.