Absolute value equations: |f(x)| = c removes absolute value by cases. Case analysis: when f(x) ≥ 0, |f(x)| = f(x); when f(x) < 0, |f(x)| = -f(x). Solution approach: solve both cases separately, verify solutions satisfy original conditions. Example: |x - 3| = 5 gives x - 3 = 5 or x - 3 = -5, so x = 8 or x = -2. Shortcut: |x - a| = b means x is b units away from a on number line. Common traps: forgetting to check both cases, accepting extraneous solutions. Exam tips: always verify in original equation. Time-saving: use graphical interpretation for quick answers. Applications: tolerance limits in manufacturing, distance problems. Critical points: where expression inside absolute value equals zero. Graph interpretation: V-shaped with vertex at critical point. Understanding absolute value geometry helps avoid careless errors.