Equations with two linear moduli

|u|=|v| is equivalent to u=v or u=-v, since both sides are nonnegative and their squares are equal. Solve the equal-inner and opposite-inner equations separately; unite their solutions and remove duplicates. Check for a contradiction or identity in either branch. For |2x+1|=|x-2|, the branches give x=-3 and x= 13. Check: do not require x-2 0 in this example: the right side is already an absolute value. Opposite inner expressions give equality for every input.