Step 1: Identify the type — pure quadratic inequality, modulus equation, modulus inequality, or combination. Step 2: For quadratic inequalities, find discriminant and roots, then use sign analysis. Step 3: For modulus expressions, identify critical points and split into cases. Step 4: Solve each case and take the union of valid solutions. Step 5: For compound expressions, consider squaring (when both sides non-negative) or substitution (t=|x|). Common pitfalls: forgetting that |x|=t gives two solutions (+/-t), not checking that solutions lie in the assumed interval, and mishandling strict vs non-strict inequalities at boundary points. Time: these problems should take 2-3 minutes. If case-splitting gets complicated, try the squaring approach or graphical reasoning.