Advanced equation solving combines multiple techniques for complex problems. Equations with absolute values |ax + b| = c: Split into ax + b = c or ax + b = -c, solve both. Example: |2x - 3| = 5 → 2x - 3 = 5 (x=4) or 2x - 3 = -5 (x=-1). Reciprocal equations: If x appears with 1/x, substitute y = x + 1/x. Parametric equations: One variable expressed via parameter. Equations with multiple variables: Treat systematically using substitution. Shortcut: Identify equation type; choose method accordingly. Exam tip: Check all solutions satisfy domain restrictions (e.g., denominators ≠ 0, arguments of logs > 0).