Core rules: |f(x)| < a ↔ -a < f(x) < a (intersection). |f(x)| > a ↔ f(x)<-a or f(x)>a (union). For |f(x)| < |g(x)|: square both sides (valid since both sides non-negative): $f^2$ < $g^2$, i.e., (f-g)(f+g) < 0. Apply wavy curve to the product. For compound modulus inequalities like |x-1|+|x+3| > 6: use case-splitting at critical points or the geometric (distance) interpretation. Special: |f(x)|<0 has no solution; |f(x)|<=0 iff f(x)=0; |f(x)|>=0 is always true.