3 5 Compound Inequalities Essential Question How do

  • Slides: 15
Download presentation
3. 5 Compound Inequalities Essential Question: How do you solve and graph inequalities with

3. 5 Compound Inequalities Essential Question: How do you solve and graph inequalities with “and” and “or”? ? ? ?

Vocabulary • Compound inequality-when two simple inequalities are combined into one statement by words

Vocabulary • Compound inequality-when two simple inequalities are combined into one statement by words AND or OR. • Intersection- overlapping region of two numbers lines and shows solutions to both inequalities. (AND) • Union- two regions and shows solutions of either inequality. (OR) ? ? ?

Example-Writing Compound Inequalities from Graph • Use the shaded region as the key. •

Example-Writing Compound Inequalities from Graph • Use the shaded region as the key. • If the shaded portion is: – Between two values AND (2 ways to write them) – Not between two values OR ? ? ?

Practice • Write the compound inequality shown by each graph. Write the AND two

Practice • Write the compound inequality shown by each graph. Write the AND two ways. ? ? ?

Intersection • AND inequalities are segments ? ? ?

Intersection • AND inequalities are segments ? ? ?

Example-Intersections (AND) • Solve using AND and the other by inverse operations. Graph solutions.

Example-Intersections (AND) • Solve using AND and the other by inverse operations. Graph solutions. ? ? ?

Intersections (AND) • Every solution of a compound inequality involving AND must be a

Intersections (AND) • Every solution of a compound inequality involving AND must be a solution of both parts of the compound inequality. • If no numbers are solutions of both simple inequalities, then the compound inequality has no solutions. ? ? ?

Practice • Solve a using AND and b using inverse operations. Graph solutions. ?

Practice • Solve a using AND and b using inverse operations. Graph solutions. ? ? ?

Union • OR inequalities are opposite rays ? ? ?

Union • OR inequalities are opposite rays ? ? ?

Example- Union (OR) • Solve and graph solutions. • OR inequalities typically have OR

Example- Union (OR) • Solve and graph solutions. • OR inequalities typically have OR in them ? ? ?

Example- Union (OR) • The solutions of a compound inequality involving OR are not

Example- Union (OR) • The solutions of a compound inequality involving OR are not always two separate sets of numbers. This is rare, but not impossible. • Some numbers may be solutions of both parts of the compound inequality. ? ? ?

Practice • Solve and graph solutions. ? ? ?

Practice • Solve and graph solutions. ? ? ?

Review • Which compound inequality is an intersection and which is a union? •

Review • Which compound inequality is an intersection and which is a union? • What does the AND inequality and OR inequality look like? • What are the two ways you can write an AND inequality solution? ? ? ?

Review • Solve and graph the inequalities. ? ? ?

Review • Solve and graph the inequalities. ? ? ?

Summary • Answer the essential question in detailed, complete sentences. How do you solve

Summary • Answer the essential question in detailed, complete sentences. How do you solve and graph inequalities with “and” and “or”? • Write 2 -3 study questions in the left column to correspond with the notes. ? ? ?