The wavy curve (method of intervals) solves polynomial and rational inequalities. Steps: (1) Factor the expression completely. (2) Mark all zeros on a number line. (3) Determine the sign in the rightmost interval (usually positive for positive leading coefficient). (4) Alternate signs at each simple root. (5) At repeated roots with even multiplicity, sign does NOT change; odd multiplicity, sign changes. (6) For rational inequalities, denominator zeros are excluded from the solution. Example: (x-1)^2$\frac{x-3}{(x+2)}$ > 0. Roots: x=1(even), x=3(odd), x=-2(odd). Rightmost sign: positive (for x>3). Moving left: (1,3) negative (sign change at 3), (-2,1) negative (no change at 1, even), (-inf,-2) positive. Solution: (-inf,-2) union (3,inf). x=1 not included since expression=0 there.