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Part of 1966 Czech and Slovak Olympiad III A

Problems(1)

Inequalities with absolute value

Source: Czech and Slovak Olympiad 1966, National Round, Problem 1

Consider a system of inequalities \begin{align*}y-x&\ge|x+1|-|x-1|, \\ |y&-x|-y+x\ge2.\end{align*} Draw solutions of each inequality in the plane separately and highlight solution of the system.

inequalitiesabsolute valuealgebra