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Intersection of IntervalsThis presentation will focus on compound inequalities using the word and. A compound inequality is formed when two inequalities are joined using either the word and or the word or.

An example of such a compound inequality is

When working with a compound inequality, think intersection.The intersection of two sets is the set of elements that are common to both sets. The symbol is used to represent intersection.

Consider how two streets come together to demonstrate this concept.The intersection of the two streets is the portion of pavement that is common to both.Harmony StreetShields Street

Example 1Find the intersection of the two inequalities:

andWe want to find the values of x that are common to both inequalities.A graph will assist in accomplishing this.

Graph the points on the line that are common to both graphs.The solution is

The interval notation answer is

Example 2Find the intersection of the two inequalities:

andWe want to find the values of x that are common to both inequalities.A graph will assist in accomplishing this.

Graph the points on the line that are common to both graphs.The solution is

The interval notation answer is

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