Problem 1 - Entrance Test

1. Split the inequality into two cases: x² - 3x + 2 ≥ 0 and x² - 3x + 2 < 0. 2. For the first case, solve x² - 3x + 2 ≤ x + 2 → x² - 4x ≤ 0 → x(x - 4) ≤ 0 → x ∈ [0, 4]. 3. For the second case, -(x² - 3x + 2) ≤ x + 2 → x² - 3x + 2 ≥ -x - 2 → x² - 2x + 4 ≥ 0, which is always true. 4. Intersect with the domain x² - 3x + 2 < 0 (x ∈ (1, 2)). Final solution: x ∈ [0,4] ∩ [–∞,1] ∪ (1,2) → x ∈ [0,2] ∪ (1,2) → x ∈ [0,2]. Correct answer is C if adjusted, but since the options need correction, the correct interval is x ∈ [0,2].