3.6 Solving Compound Inequalities. Language Goal  Students will be able to read and say compound inequalities. Math Goal  Students will be able to solve.

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3.6 Solving Compound Inequalities

Language Goal  Students will be able to read and say compound inequalities. Math Goal  Students will be able to solve and graph compound inequalities. Essential Question  What are the differences between the graphs of an inequality and a compound inequality?

 Good Luck!  You will do great!

 Compound Inequality  Intersection  Union When two simple inequalities are combined into one statement by the words AND or OR. Example: x > 3 and x < -2 A compound inequality involving AND by using the idea of an overlapping region. Shows the numbers that are solutions of both inequalities. A compound inequality involving OR by using the idea of combining regions. Shows the numbers that are solutions of either inequality.

WordsAlgebraGraph All real numbers greater than 2 AND less than 6 x > 2 AND x < 6 2 < x < 6 All real numbers greater than or equal to 2 And less than or equal to 6 All real numbers less than 2 OR greater than 6 x 6 All real numbers less than or equal to 2 OR greater than or equal to 6

 A water analyses recommends that the pH level of swimming pool water be between 7.2 and 7.6 inclusive. Write a compound inequality to show the pH levels that are within the recommended range. Graph the solution.

 The free chlorine level in a pool should be between 1.0 and 3.0 parts per million inclusive. Write a compound inequality to show the levels that are within this range. Graph the solution.

 The pH of a popular shampoo is between 6.0 and 6.5 inclusive. Write a compound inequality to show the pH levels of this shampoo. Graph the solution.

 Write the compound inequality shown by each graph. 1. 2.

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