3-6 Solving Compound Inequalities
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1 Warm Up Solve each inequality. 1. x < 2x + 3 Solve each inequality and graph the solutions. 3. 4x x + 3
2 Learning Targets Solve compound inequalities with one variable. Graph solution sets of compound inequalities with one variable.
3 compound inequality intersection union Fancy Math Words
4 The inequalities you have seen so far are simple inequalities. When two simple inequalities are combined into one statement by the words AND or OR, the result is called a compound inequality.
5
6 Example 1: Chemistry Application The ph level 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 solutions. Define the variable: Let p be the ph level of the shampoo
7 Check It Out! Example 1 The free chlorine 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 solutions. Define the variable: Write the compound inequality:
8 You can graph the solutions of a compound inequality involving AND by using the idea of an overlapping region. The overlapping region is called the intersection and shows the numbers that are solutions of both inequalities.
9 Example 2A: Solving Compound Inequalities Involving AND Solve the compound inequality and graph the solutions. 5 < x + 1 <
10 Example 2B: Solving Compound Inequalities Involving AND Solve the compound inequality and graph the solutions. 8 < 3x
11 Solve the compound inequality and graph the solutions. 9 < x 10 < 5 You Try! Example 2a
12 You Try! Example 2b Solve the compound inequality and graph the solutions. 4 3n + 5 <
13 You can graph the solutions of a compound inequality involving OR by using the idea of combining regions. The combine regions are called the union and show the numbers that are solutions of either inequality. >
14 Example 3A: Solving Compound Inequalities Involving OR Solve the inequality and graph the solutions. 8 + t 7 OR 8 + t <
15 Example 3B: Solving Compound Inequalities Involving OR Solve the inequality and graph the solutions. 4x 20 OR 3x >
16 You Try! Example 3a Solve the compound inequality and graph the solutions. 2 +r < 12 OR r + 5 >
17 Solve the compound inequality and graph the solutions. 7x 21 OR 2x < 2 You Try! Example 3b
18 Example 4A: Writing a Compound Inequality from a Graph Write the compound inequality shown by the graph.
19 Example 4B: Writing a Compound Inequality from a Graph Write the compound inequality shown by the graph.
20 You Try! Example 4b Write the compound inequality shown by the graph.
21 You Try! Example 4a Write the compound inequality shown by the graph.
22 Lesson Quiz: Part I 1. The target heart rate during exercise for a 15 year-old is between 154 and 174 beats per minute inclusive. Define a variable. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions.
23 Lesson Quiz: Part II Solve each compound inequality and graph the solutions w r > 2 OR 3 + r < 7
24 Lesson Quiz: Part III Write the compound inequality shown by each graph
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