Combined Inequalities

Students learn that when solving a combined inequality in the form x < -3 or x > 2, "or" means "union", or everything that's mentioned in the two inequalities. And when solving a combined inequality in the form x < -3 and x > 2, "and" means "intersection", or only what's in common to the two inequalities. So when graphing a combined inequality, the first step is to graph the inequalities above the number line, then combine them on the number line based on "or" (bring everything down to the number line) or "and" (only bring down the parts where the graphs overlap).

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