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# Compound Inequalities

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In this section, we will learn about compound inequalities. These are inequalities that are linked with a connective word such as "and" or "or". In order to understand the solution set for these two types of compound inequalities, we think back to the union and intersection of two sets. The union of two sets A and B consists of all elements of A and B, with no individual element listed more than once. As an example, suppose set A = {3,5,7} and set B = {7,9,14}: the union of set A and B would be: A ∪ B = {3,5,7,9,14}. Notice how the element 7 appears in both sets but is listed only once. The intersection of the same two sets A and B consists of all elements that are common to both A and B. The intersection of sets A and B would be A ∩ B = {7}. This is because 7 is the only element common to both sets A and B. Once we understand the concepts of intersection and union, we are ready to push into an understanding of compound inequalities. A solution for a compound inequality with "and" consists of all numbers that satisfy both inequalities. This is the intersection of the two solution sets. The solution for a compound inequality with "or" consists of all numbers that are solutions to either inequality. This is the union of the two solutions sets.
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