 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-1/8/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Evaluate the absolute values on the three intervals separated by one and two:

∣ x - 2∣ + ∣ x - 1∣ = ⎩ ⎨ ⎧ 3 - 2 x, 1, 2 x - 3, x < 1, 1 \leq x \leq 2, x > 2.

The strict inequality therefore holds precisely for

x < 1 or x > 2.

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