Lesson 4: 5-4 Solving Compound Inequalities

Describe the steps to solve a compound inequality that is an intersection.

Describe the solution set of a compound inequality that is an intersection.

Describe the solution set of a compound inequality that is a union.

compound inequality
intersction
union

A.CED.1 Create equations and inequalitys in one variable and use them to solve problems.

A.CED.3 Represent constarins by equations or inequalities, and by system of equations and/or ineqaulities, and interpret solutions as viable or nonviable options in modeling context.

SAT questions related to inequalities: 5-4-13,7-4-5,4-4-19,8-3-6,1-4-28,5-3-7,6-3-14;

If two inequalities are joined by the words and or or, the result is a compound inequality. If a compound inequality contains the word and, the graph pf the solution is an intersection of the graphs of the two inequalities. If a compound inequality contains the word or, the graph pf the solution is the union of the graphs of the two inequalities.

In 2014, the National Museum of Natural History in Washinton D.C., displayed its first Tyrannosaurus rex skeleton in the museum's history. The fossles were discovered by a hiker in Montana and are one of the most complete T.rex skeletons ever found. The fossles are estimated to be at least 65 million years old but less than 68 million years old. This can be written as a compund inequality 65<= t<68, where t is the age of fosill in millions.

Students may assume that solution set for {xl1<=x<7} includes the 7. It does not. Less than 7 does not include 7, so the solution set does not include 7.

If some students are overwhelmed trying to discern whether word problems represent compound inequalities and whether the inequalities are inclusive or exclusive, then pair these students with more advanced students to discuss and solve Exercises 33-37. Encourage both students to take active role in solving the problems.

Practice: Exercises 1 - 5

Exercises 37-43

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