For |f(x)| = a (a>0): split into f(x)=a and f(x)=-a. For |f(x)|=|g(x)|: square both sides or use f(x)=+/-g(x). For equations with multiple modulus terms like |x-1|+|x+2|=k: identify critical points (x=1, x=-2), split the number line into intervals, remove modulus with appropriate signs in each interval, solve the resulting equation, and verify the solution lies in the assumed interval. For nested modulus ||x|-a|=b: work from inside out, solving |x|=a+b and |x|=a-b (if a-b >= 0). Total solutions = 2*(number of positive values) + (1 if value is 0).